estimation of controlled direct effects on a dichotomous outcome using logistic structural direct effect models we consider the problem of assessing whether an exposure affects a dichotomous outcome other than by modifying a given mediator the standard approach logistic regression adjusting for both exposure and the mediator is known to be biased in the presence of confounders for the mediator outcome relationship because additional regression adjustment for such confounders is only justified when they are not affected by the exposure inverse probability weighting has been advocated but is not ideally tailored to mediators that are continuous or have strong measured predictors we overcome this limitation by developing inference for a novel class of causal models that are closely related to robins logistic structural direct effect models but do not inherit their difficulties of estimation we study identification and efficient estimation under the assumption that all confounders for the exposure outcome and mediator outcome relationships have been measured and find adequate performance in simulation studies we discuss extensions to case control studies and relevant implications for the generic problem of adjustment for time varying confounding

model for coarsening froths and foams the coarsening process of froths and foams is described statistically in two dimensions by a random neighbor model this nonlinear dynamical model contains no free parameters all rates are determined dynamically it describes normal growth agrees with experimental results throws light on old data and hopefully inspires new simulations and measurements lewis s law anat rec 38 341 1928 am j bot 30 74 1943 and some other properties can be derived analytically from the model

estimation and inference for distribution functions and quantile functions in treatment effect models abstract we propose inverse probability weighted estimators for the distribution functions of the potential outcomes under the unconfoundedness assumption and apply the inverse mapping to obtain the quantile functions we show that these estimators converge weakly to zero mean gaussian processes a simulation method is proposed to approximate these limiting processes based on these results we construct tests for stochastic dominance relations between the potential outcomes monte carlo simulations are conducted to examine the finite sample properties of our tests we apply our test in an empirical example and find that a job training program had a positive effect on incomes

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data which involve models for both the propensity score and the regression of outcome on covariates the usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods even with some estimated propensity scores close to zero

a framework for bayesian nonparametric inference for causal effects of mediation we propose a bayesian non parametric bnp framework for estimating causal effects of mediation the natural direct and indirect effects the strategy is to do this in two parts part 1 is a flexible model using bnp for the observed data distribution part 2 is a set of uncheckable assumptions with sensitivity parameters that in conjunction with part 1 allows identification and estimation of the causal parameters and allows for uncertainty about these assumptions via priors on the sensitivity parameters for part 1 we specify a dirichlet process mixture of multivariate normals as a prior on the joint distribution of the outcome mediator and covariates this approach allows us to obtain a simple closed form of each marginal distribution for part 2 we consider two sets of assumptions a the standard sequential ignorability imai et al 2010 and b weakened set of the conditional independence type assumptions introduced in daniels et al 2012 and propose sensitivity analyses for both we use this approach to assess mediation in a physical activity promotion trial

identification and efficient estimation of the natural direct effect among the untreated the natural direct effect nde or the effect of an exposure on an outcome if an intermediate variable was set to the level it would have been in the absence of the exposure is often of interest to investigators in general the statistical parameter associated with the nde is difficult to estimate in the non parametric model particularly when the intermediate variable is continuous or high dimensional in this paper we introduce a new causal parameter called the natural direct effect among the untreated discus identifiability assumptions propose a sensitivity analysis for some of the assumptions and show that this new parameter is equivalent to the nde in a randomized controlled trial we also present a targeted minimum loss estimator tmle a locally efficient double robust substitution estimator for the statistical parameter associated with this causal parameter the tmle can be applied to problems with continuous and high dimensional intermediate variables and can be used to estimate the nde in a randomized controlled trial with such data additionally we define and discuss the estimation of three related causal parameters the natural direct effect among the treated the indirect effect among the untreated and the indirect effect among the treated

nonparametric iv estimation of local average treatment effects with covariates in this paper nonparametric instrumental variable estimation of local average treatment effects late is extended to incorporate covariates estimation of late is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models including covariates in the estimation of late is necessary when the instrumental variable itself is confounded such that the iv assumptions are valid only conditional on covariates previous approaches to handle covariates in the estimation of late relied on parametric or semiparametric methods in this paper a nonparametric estimator for the estimation of late with covariates is suggested that is root n asymptotically normal and efficient

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

mean field theory for coarsening faceted surfaces a mean field theory is developed for the scale invariant length distributions observed during the coarsening of generic one dimensional faceted surfaces this theory closely follows the lifshitz slyozov wagner theory of ostwald ripening in two phase systems but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling work on particle coalescence and induces an unexpected coupling between the convolution and the rate of facet loss as a generic framework the theory concisely illustrates how the universal processes of facet removal and neighbor merger are moderated by the system specific mean field velocity describing average rates of length change for a simple example facet dynamics associated with the directional solidification of a binary alloy agreement between the predicted scaling state and that observed after direct numerical simulation of 40 000 000 facets is reasonable given the limiting assumption of noncorrelation between neighbors relaxing this assumption is a clear path forward toward improved quantitative agreement with data in the future

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

scaling probability key to the equilibrium statistical volume distribution in foams abstract the equilibrium statistical volume distribution in foams which has been previously demonstrated to be the so called log normal is accounted on probability grounds by a scaling law on the bubble s volume time evolution this law states that the conditional probability for a given bubble to have the volume v t t he assumption that it was v t to depend solely on the relationship v t t v t and in particular to be independent of the time t the theoretical results however allow to go further indeed since the time dependece of its parameters expectation and variance are given functions of time only two parameters are necessary to describe completely the foam

on the role of the propensity score in efficient semiparametric estimation of average treatment effects in this paper the role of the propensity score in the efficient estimation of average treatment effects is examined under the assumption that the treatment is ignorable given some observed characteristics it is shown that the propensity score is ancillary for estimation of the average treatment effects the propensity score is not ancillary for estimation of average treatment effects on the treated it is suggested that the marginal value of the propensity score lies entirely in the dimension reduction efficient semiparametric estimators of average treatment effects and average treatment effects on the treated are shown to take the form of relevant sample averages of the data completed by the nonparametric imputation method it is shown that the projection on the propensity score is not necessary for efficient semiparametric estimation of average treatment effects on the treated even if the propensity score is known an application to the experimental data reveals that conditioning on the propensity score may even result in a loss of efficiency

mediation analysis with time varying exposures and mediators in this paper we consider causal mediation analysis when exposures and mediators vary over time we give non parametric identification results discuss parametric implementation and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models we also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models when there are time varying confounders affected by prior exposure and mediator natural direct and indirect effects are not identified however we define a randomized interventional analogue of natural direct and indirect effects that are identified in this setting the formula that identifies these effects we refer to as the mediational g formula when there is no mediation the mediational g formula reduces to robins regular g formula for longitudinal data when there are no time varying confounders affected by prior exposure and mediator values then the mediational g formula reduces to a longitudinal version of pearl s mediation formula however the mediational g formula itself can accommodate both mediation and time varying confounders and constitutes a general approach to mediation analysis with time varying exposures and mediators

bias reduced doubly robust estimation over the past decade doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models these are asymptotically unbiased when at least one of two nuisance working models is correctly specified regardless of which while their asymptotic distribution is not affected by the choice of root n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified this choice of estimators can have a dramatic impact under misspecification of at least one working model in this article we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models which is designed to improve the performance of the doubly robust estimator of interest relative to the default use of maximum likelihood estimators for the nuisance parameters the proposed approach locally minimizes the squared first order asymptotic bias of the doubly robust estim

causal mediation analysis with multiple mediators in diverse fields of empirical research including many in the biological sciences attempts are made to decompose the effect of an exposure on an outcome into its effects via a number of different pathways for example we may wish to separate the effect of heavy alcohol consumption on systolic blood pressure sbp into effects via body mass index bmi via gamma glutamyl transpeptidase ggt and via other pathways much progress has been made mainly due to contributions from the field of causal inference in understanding the precise nature of statistical estimands that capture such intuitive effects the assumptions under which they can be identified and statistical methods for doing so these contributions have focused almost entirely on settings with a single mediator or a set of mediators considered en bloc in many applications however researchers attempt a much more ambitious decomposition into numerous path specific effects through many mediators in this article we give counterfactual definitions of such path specific estimands in settings with multiple mediators when earlier mediators may affect later ones showing that there are many ways in which decomposition can be done we discuss the strong assumptions under which the effects are identified suggesting a sensitivity analysis approach when a particular subset of the assumptions cannot be justified these ideas are illustrated using data on alcohol consumption sbp bmi and ggt from the izhevsk family study we aim to bridge the gap from single mediator theory to multiple mediator practice highlighting the ambitious nature of this endeavor and giving practical suggestions on how to proceed

doubly robust estimation in missing data and causal inference models the goal of this article is to construct doubly robust dr estimators in ignorable missing data and causal inference models in a missing data model an estimator is dr if it remains consistent when either but not necessarily both a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified because with observational data one can never be sure that either a missingness model or a complete data model is correct perhaps the best that can be hoped for is to find a dr estimator dr estimators in contrast to standard likelihood based or nonaugmented inverse probability weighted estimators give the analyst two chances instead of only one to make a valid inference in a causal inference model an estimator is dr if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct inference based on dr estimators should improve upon previous approaches indeed we present the results of simulation studies which demonstrate that the finite sample performance of dr estimators is as impressive as theory would predict the proposed method is applied to a cardiovascular clinical trial

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

uniformly semiparametric efficient estimation of treatment effects with a continuous treatment this article studies identification estimation and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption we show identification of the parameters of interest the dose response functions under the assumption that selection to treatment is based on observables we propose a semiparametric two step estimator and consider estimation of the dose response functions through moment restriction models with generalized residual functions that are possibly nonsmooth this general formulation includes average and quantile treatment effects as special cases the asymptotic properties of the estimator are derived namely uniform consistency weak convergence and semiparametric efficiency we also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice monte carlo simulations show that the proposed methods have good finite sample properties finally we apply the proposed

a variational principle for markov processes in this note we first present a result concerning a variational principle for general markov processes then we apply it to spin particle systems to obtain a full form of a variational principle characterizing the stationary markov laws of the systems a related extreme decomposition for any stationary distribution of such markov systems is also given

bounded efficient and multiply robust estimation of average treatment effects using instrumental variables instrumental variables ivs are widely used for estimating causal effects in the presence of unmeasured confounding under the standard iv model however the average treatment effect ate is only partially identifiable to address this we propose novel assumptions that allow for identification of the ate our identification assumptions are clearly separated from model assumptions needed for estimation so that researchers are not required to commit to a specific observed data model in establishing identification we then construct multiple estimators that are consistent under three different observed data models and multiply robust estimators that are consistent in the union of these observed data models we pay special attention to the case of binary outcomes for which we obtain bounded estimators of the ate that are guaranteed to lie between 1 and 1 our approaches are illustrated with simulations and a data analysis evaluating the causal effect of education on earnings

modelling froth dynamics persistence measures the soap froth provides an idealised example of a cellular structure which evolves or coarsens over laboratory time scales and for which topological measures appear to provide an intuitive characterisation however froth is an intrinsically non equilibrium system and topological measures are not universally applicable to such processes recently persistence has been proposed as a more general probe of non equilibrium dynamics where the froth is viewed as a two phase system through construction of a virtual phase we use a direct simulation method to investigate persistence for random 2 d voronoi and hexagonal froths of size up to 2500 bubbles we find that simulation results are qualitatively similar to those of experiment with the normalised average area a t a 0 of persistent regions within a bubble at time t approaching an equilibrium value for a range of volume or sampling fraction values for the voronoi froth the case for the hexagonal is less clear since exclusion of the defect or defects from the virtual phase leads to rapid decline in the average area of persistent bubbles simulation times required are very long however and evolution is slow for long term survivors consequently persistent behaviour is not demonstrated satisfactorily for the fraction of survivors n t n t in a random system of this size although for the hexagonal with one or more seeded defects there is some indication that decay depends on for some colouring patterns however limiting slope values are probably not established

scaling properties of three dimensional foams we obtain the scaling states of three dimensional soap foams by using equilibrium statistical mechanics techniques we consider a phase space where each bubble is characterized by its center of mass position volume surface and number of faces a gibbs entropy function is then defined and as done in standard statistical mechanics we obtain the probability density function defined in the phase space by maximizing the entropy subject to convenient constraints the froth is supposed to completely fill the available volume and we consider energy terms accounting for surface tension and the thermal energy of the gas inside the bubbles we find that the volume distribution presents an exponential decay with cell size and the correlation between cell volume and number of faces fits very well the available numerical data additional distribution functions and average values are also in good agreement with numerical simulations

counterfactual links to the proportion of treatment effect explained by a surrogate marker in a randomized clinical trial a statistic that measures the proportion of treatment effect on the primary clinical outcome that is explained by the treatment effect on a surrogate outcome is a useful concept we investigate whether a statistic proposed to estimate this proportion can be given a causal interpretation as defined by models of counterfactual variables for the situation of binary surrogate and outcome variables two counterfactual models are considered both of which include the concept of the proportion of the treatment effect which acts through the surrogate in general the statistic does not equal either of the two proportions from the counterfactual models and can be substantially different conditions are given for which the statistic does equal the counterfactual model proportions a randomized clinical trial with potential surrogate endpoints is undertaken in a scientific context this context will naturally place constraints on the parameters of the counterfactual model we conducted a simulation experiment to investigate what impact these constraints had on the relationship between the proportion explained pe statistic and the counterfactual model proportions we found that observable constraints had very little impact on the agreement between the statistic and the counterfactual model proportions whereas unobservable constraints could lead to more agreement

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

geometrical consequences of foam equilibrium equilibrium conditions impose nontrivial geometrical constraints on the configurations that a two dimensional foam can attain in the first place the three centers of the films that converge to a vertex have to be on a line i e all vertices are aligned moreover an equilibrated foam must admit a reciprocal figure this means that it must be possible to find a set of points mathrm p mathrm i on the plane one per bubble such that the segments mathrm p mathrm i mathrm p mathrm j are normal to the corresponding foam films it is furthermore shown that these constraints are equivalent to the requirement that the foam be a sectional multiplicative vorono ifmmode imath else i fi umlaut partition smvp a smvp is a cut with a two dimensional plane of a three dimensional multiplicative vorono ifmmode imath else i fi umlaut partition thus given an arbitrary equilibrated foam we can always find pointlike sources one per bubble in three dimensions that reproduce this foam as a generalized vorono ifmmode imath else i fi umlaut partition these sources are the only degrees of freedom that we need in oder to describe the foam fully

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

edge scaling of soap froth abstract we investigate the scaling properties of the edge distribution of soap froth and compare it with the area scaling law the data collapse for edge scaling of cells belonging to the same topological class is explained by a harmonic expansion of the energy of the froth with area perimeter constraint the edge scaling hypothesis is found to be comparable to area scaling the implication on existing theories for the evolution of soap froth is discussed

inverse probability weighted estimation for general missing data problems abstract i study inverse probability weighted m estimation under a general missing data scheme examples include m estimation with missing data due to a censored survival time propensity score estimation of the average treatment effect in the linear exponential family and variable probability sampling with observed retention frequencies i extend an important result known to hold in special cases estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation for the treatment effect case the setup allows a general characterization of a double robustness result due to scharfstein et al 1999 rejoinder journal of the american statistical association 94 1135 1146

sensitivity analysis for unobserved confounding of direct and indirect effects using uncertainty intervals to estimate direct and indirect effects of an exposure on an outcome from observed data strong assumptions about unconfoundedness are required since these assumptions cannot be tested using the o

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

covariate selection for the nonparametric estimation of an average treatment effect observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology such studies often rel

dynamics of soap froth abstract the coarsening process of soap froths is described statistically in two dimensions by a random neighbour model this non linear dynamical model contains no free parameters it describes normal growth with distributions that agree with experimental results

estimation of mediation effects for zero inflated regression models the goal of mediation analysis is to identify and explicate the mechanism that underlies a relationship between a risk factor and an outcome via an intermediate variable mediator in this paper we consider the estimation of mediation effects in zero inflated zi models intended to accommodate extra zeros in count data focusing on the zi negative binomial zinb models we provide a mediation formula approach to estimate the overall mediation effect in the standard two stage mediation framework under a key sequential ignorability assumption we also consider a novel decomposition of the overall mediation effect for the zi context using a three stage mediation model estimation of the components of the overall mediation effect requires an assumption involving the joint distribution of two counterfactuals simulation study results demonstrate low bias of mediation effect estimators and close to nominal coverage probability cp of confidence intervals we also modify the mediation formula method by replacing exact integration with a monte carlo integration method the method is applied to a cohort study of dental caries in very low birth weight adolescents for overall mediation effect estimation sensitivity analysis was conducted to quantify the degree to which key assumption must be violated to reverse the original conclusion

matching and semi parametric iv estimation a distance based measure of migration and the wages of young men abstract our paper estimates the effect of us internal migration on wage growth for young men between their first and second job our analysis of migration extends previous research by i exploiting the distance based measures of migration in the national longitudinal surveys of youth 1979 nlsy79 ii allowing the effect of migration to differ by schooling level and iii using propensity score matching to estimate the average treatment effect on the treated atet for movers and iv using local average treatment effect late estimators with covariates to estimate the average treatment effect ate and atet for compliers we believe the conditional independence assumption cia is reasonable for our matching estimators since the nlsy79 provides a relatively rich array of variables on which to match our matching methods are based on local linear local cubic and local linear ridge regressions local linear and local ridge regression matching produce relatively similar point estimates and standard errors while local cubic regression matching badly over fits the data and provides very noisy estimates we use the bootstrap to calculate standard errors since the validity of the bootstrap has not been investigated for the matching estimators we use and has been shown to be invalid for nearest neighbor matching estimators we conduct a monte carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching the data generating processes in our monte carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values the estimated standard errors from the bootstrap are very close to those from the monte carlo experiments which lends support to our using the bootstrap to calculate standard errors in our setting from the matching estimators we find a significant positive effect of migration on the wage growth of college graduates and a marginally significant negative effect for high school dropouts we do not find any significant effects for other educational groups or for the overall sample our results are generally robust to changes in the model specification and changes in our distance based measure of migration we find that better data matters if we use a measure of migration based on moving across county lines we overstate the number of moves while if we use a measure based on moving across state lines we understate the number of moves further using either the county or state measures leads to much less precise estimates we also consider semi parametric late estimators with covariates frolich 2007 using two sets of instrumental variables we precisely estimate the proportion of compliers in our data but because we have a small number of compliers we cannot obtain precise late estimates

robust inference on population indirect causal effects the generalized front door criterion standard methods for inference about direct and indirect effects require stringent no unmeasured confounding assumptions which often fail to hold in practice particularly in observational studies the goal of the paper is to introduce a new form of indirect effect the population intervention indirect effect that can be non parametrically identified in the presence of an unmeasured common cause of exposure and outcome this new type of indirect effect captures the extent to which the effect of exposure is mediated by an intermediate variable under an intervention that holds the component of exposure directly influencing the outcome at its observed value the population intervention indirect effect is in fact the indirect component of the population intervention effect introduced by hubbard and van der laan interestingly our identification criterion generalizes judea pearl s front door criterion as it does not require no direct effect of exposure not mediated by the intermediate variable for inference we develop both parametric and semiparametric methods including a novel doubly robust semiparametric locally efficient estimator that perform very well in simulation studies finally the methods proposed are used to measure the effectiveness of monetary saving recommendations among women enrolled in a maternal health programme in tanzania

large deviations for empirical processes of interacting particle systems in this paper we study process level large deviations for spin flip particle systems and more general markov processes we prove that a modification of a well known donsker varadhan entropy function can be used to govern the large deviation lower bounds for any such process starting from a class of initial distributions related to an extremal invariant measure of the process in some specific cases we obtain the full large deviation principle

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

scaling state in froths deduced from a corrected von neumann s law abstract a corrected and generalized von neumann s law is proposed so that its statistical consequences agree with all experiments reported in the literature it is shown that a froth s scaling state concerning the surface area distribution may be deduced from the stochastical independence between the number of sides distribution and the bubbles surface area and on the simple change of von neumann s law from da dt k n 6 to da dt ka n 6

simple least squares estimator for treatment effects using propensity score residuals summary propensity score matching is widely used to control covariates when analysing the effects of a nonrandomized binary treatment however it requires several arbitrary decisions such as how many matched subjects to use and how to choose them in this paper a simple least squares estimator is proposed where the treatment and possibly the response variable is replaced by the propensity score residual the proposed estimator controls covariates semiparametrically if the propensity score function is correctly specified furthermore it is numerically stable and relatively easy to use compared with alternatives such as matching regression imputation weighting and doubly robust estimators the proposed estimator also has a simple valid asymptotic variance estimator that works well in small samples the least squares estimator is extended to multiple treatments and noncontinuously distributed responses a simulation study demonstrates that it has lower mean squared error than its competitors

estimation of controlled direct effects in time varying treatments using structural nested mean models application to a primary prevention trial for coronary events with pravastatin for the estimation of controlled direct effects i e direct effects controlling intermediates that are set at a fixed level for all members of the population without bias two fundamental assumptions must hold the absence of unmeasured confounding factors for treatment and outcome and for intermediate variables and outcome even if these assumptions hold one would nonetheless fail to estimate direct effects using standard methods for example stratification or regression modeling when the treatment influences confounding factors for such situations the sequential g estimation method for structural nested mean models has been developed for estimating controlled direct effects in point treatment situations in this study we demonstrate that this method can be applied to longitudinal data with time varying treatments and repeatedly measured intermediate variables we sequentially estimate the parameters in two structural nested mean models one for a repeatedly measured intermediate and the other one for direct effects of a time varying treatment the method was applied to data from a large primary prevention trial for coronary events in which pravastatin was used to lower the cholesterol levels in patients with moderate hypercholesterolemia

multiply robust causal inference with double negative control adjustment for categorical unmeasured confounding unmeasured confounding is a threat to causal inference in observational studies in recent years the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity negative controls have a long standing tradition in laboratory sciences and epidemiology to rule out non causal explanations although they have been used primarily for bias detection recently miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non parametrically the average treatment effect ate from observational data subject to uncontrolled confounding we establish non parametric identification of the ate under weaker conditions in the case of categorical unmeasured confounding and negative control variables we also provide a general semiparametric framework for obtaining inferences about the ate while leveraging information about a possibly large number of measured covariates in particular we derive the semiparametric efficiency bound in the non parametric model and we propose multiply robust and locally efficient estimators when non parametric estimation may not be feasible we assess the finite sample performance of our methods in extensive simulation studies finally we illustrate our methods with an application to the post licensure surveillance of vaccine safety among children

a geometric model for anisotropic crystal growth equilibrium crystal shapes are defined uniquely by the wulff construction the classical kinematic theory of crystal growth due mainly to frank and chernov provides a mathematically equivalent prescription for the limiting growth shape to connect these two well studied states we derive a local geometric growth model and examine the transient shape evolution of an equilibrium form containing both facets and rough regions our model is appropriate to the weakly driven growth of a two dimensional single crystal with n gonal symmetry and arbitrary closed initial shape the model links disparate kinetic processes determined by the local interfacial structure to the isotropic growth drive and reproduces the experimentally observed transition from a partly rounded equilibrium shape to a highly faceted crystal which we term global kinetic faceting we solve for the transient shape dynamics globally and locally and in the latter case present a curvature evolution equation valid for any local growth law both approaches show that during kinetic faceting rough orientations grow out of existence with decreasing curvature

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

numerical simulation of two dimensional soap froth abstract the temporal evolution of two dimensional foam is studied by event driven numerical simulations based on different types of models it is shown that most of the dynamical and topological features seen in experimental measurements can be reproduced the average area of cells scales linearly with time and the distribution of n sided cells can be compared with known results the topological models regarding the lengths of the boundaries yield the best results among the models studied

augmented designs to assess principal strata direct effects summary many studies involving causal questions are often concerned with understanding the causal pathways by which a treatment affects an outcome thus the concept of direct versus indirect effects comes into play we tackle the problem of disentangling direct and indirect effects by investigating new augmented experimental designs where the treatment is randomized and the mediating variable is not forced but only randomly encouraged there are two key features of our framework we adopt a principal stratification approach and we mainly focus on principal strata effects avoiding involving a priori counterfactual outcomes using non parametric identification strategies we provide a set of assumptions which allow us to identify partially the causal estimands of interest the principal strata direct effects some examples are shown to illustrate our design and causal estimands of interest large sample bounds for the principal strata average direct effects are provided and a simple hypothetical example is used to show how our augmented design can be implemented and how the bounds can be calculated finally our augmented design is compared and contrasted with a standard randomized design

on semiparametric estimation of a path specific effect in the presence of mediator outcome confounding path specific effects constitute a broad class of mediated effects from an exposure to an outcome via one or more causal pathways along a set of intermediate variables most of the literature concerning estimation of mediated effects has focused on parametric models with stringent assumptions regarding unmeasured confounding we consider semiparametric inference of a path specific effect when these assumptions are relaxed in particular we develop a suite of semiparametric estimators for the effect along a pathway through a mediator but not through an exposure induced confounder of that mediator these estimators have different robustness properties as each depends on different parts of the likelihood of the observed data one estimator is locally semiparametric efficient and multiply robust the latter property implies that machine learning can be used to estimate nuisance functions we demonstrate these properties as well as finite sample properties of all the estimators in a simulation study we apply our method to an hiv study in which we estimate the effect comparing two drug treatments on a patient s average log cd4 count mediated by the patient s level of adherence but not by previous experience of toxicity which is clearly affected by which treatment the patient is assigned to and may confound the effect of the patient s level of adherence on their virologic outcome

a specification test for the propensity score using its distribution conditional on participation propensity score matching has become a popular method for the estimation of average treatment effects in empirical applications researchers almost always impose a parametric model for the propensity score this practice raises the possibility that the model for the propensity score is misspecified and therefore the propensity score matching estimator of the average treatment effect may be inconsistent we show that the common practice of calculating estimates of the densities of the propensity score conditional on the participation decision provides a means for examining whether the propensity score is misspecified in particular we derive a restriction between the density of the propensity score among participants and the density among nonparticipants we show that this restriction between the two conditional densities is equivalent to a particular orthogonality restriction and derive a formal test based upon it the resulting test is shown via a simulation study to have dramatically greater power than competing tests for many alternatives the principal disadvantage of this approach is loss of power against some alternatives

large deviations and ergodicity for spin particle systems in this paper we investigate the large deviation principle ldp for spin particle systems with possibly vanishing flip rates the situation turns out to be much more complicated if the flip rates are allowed to be zero than the one considered by dai where the systems are assumed to have strictly positive flip rates the upper and lower large deviation bounds are studied respectively the two governing rate functions are compared and a variational principle is given we then apply the results to obtain some new large deviation estimates for the occupation times of attractive systems in particular we prove a strong form of exponential convergence for ergodic systems

large deviation lower bounds for additive functionals of markov processes let x 1 x 2 ldots be a markov process with state space e a polish space let l n omega a n 1 sum n 1 j 0 1 a x j omega denote the normalized occupation time measure if mu is a probability measure on e g is a weak neighborhood of mu and if v subset e then we obtain asymptotic lower bounds for probabilities p x lbrack l n omega cdot in g x j omega in v 0 leq j leq n 1 rbrack in terms of i mu the rate function of donsker and varadhan our assumptions are weaker than those imposed by donsker and varadhan and the proof works without any essential change in the continuous time case as well in fact the same proofs apply to certain bounded additive functionals let r geq 0 and let f omega rightarrow mathbf b be bounded mathscr f 0 r measurable where omega is the sample space with the product topology skorohod topology in the continuous time case and mathbf b is a separable banach space let theta k omega rightarrow omega be the shift operator i e theta k omega j omega k j then we get lower bounds for probabilities involving n 1 f omega f theta 1 omega cdots f theta n 1 omega in place of l n omega cdot in this latter situation the rate function has to be the entropy function h q of donsker and varadhan

estimation of direct effects for survival data by using the aalen additive hazards model summary we extend the definition of the controlled direct effect of a point exposure on a survival outcome other than through some given time fixed intermediate variable to the additive hazard scale we propose two stage estimators for this effect when the exposure is dichotomous and randomly assigned and when the association between the intermediate variable and the survival outcome is confounded only by measured factors which may themselves be affected by the exposure the first stage of the estimation procedure involves assessing the effect of the intermediate variable on the survival outcome via aalen s additive regression for the event time given exposure intermediate variable and confounders the second stage involves applying aalen s additive model given the exposure alone to a modified stochastic process i e a modification of the observed counting process based on the first stage estimates we give the large sample properties of the estimator proposed and investigate its small sample properties by monte carlo simulation a real data example is provided for illustration

estimation of a semiparametric natural direct effect model incorporating baseline covariates establishing cause effect relationships is a standard goal of empirical science once the presence of a causal relationship is established the precise causal mechanism involved becomes a topic of interest a particularly popular type of mechanism analysis concerns questions of mediation that is to what extent an effect is direct and to what extent it is mediated by a third variable a semiparametric theory has recently been proposed which allows multiply robust estimation of direct and mediated marginal effect functionals in observational studies tchetgen tchetgen shpitser 2012 in this paper we extend the new theory to handle parametric models of natural direct and indirect effects within levels of pre exposure variables with an identity or log link function where the model for the observed data likelihood is otherwise unrestricted we show that estimation is generally not feasible in this model because of the curse of dimensionality associated with the required estimation of auxiliary conditional densities or expectations given high dimensional covariates thus we consider multiply robust estimation and propose a more general model which assumes that a subset but not all of several working models holds

inverse odds ratio weighted estimation for causal mediation analysis an important scientific goal of studies in the health and social sciences is increasingly to determine to what extent the total effect of a point exposure is mediated by an intermediate variable on the causal pathway between the exposure and the outcome a causal framework has recently been proposed for mediation analysis which gives rise to new definitions formal identification results and novel estimators of direct and indirect effects in the present paper the author describes a new inverse odds ratio weighted iorw approach to estimate so called natural direct and indirect effects the approach which uses as a weight the inverse of an estimate of the odds ratio function relating the exposure and the mediator is universal in that it can be used to decompose total effects in a number of regression models commonly used in practice specifically the approach may be used for effect decomposition in generalized linear models with a nonlinear link function and in a number of other commonly used models such as the cox proportional hazards regression for a survival outcome the approach is simple and can be implemented in standard software provided a weight can be specified for each observation an additional advantage of the method is that it easily incorporates multiple mediators of a categorical discrete or continuous nature

testing for separability in structural equations abstract separability is an important feature of structural equations as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation this paper provides a nonparametric test for separability in structural equations the test is based on a conditional independence test recently developed by huang et al 2013 building on consistent procedures of bierens 1982 1990 and stinchcombe and white 1998 the test is easy to implement and achieves n local power we apply our test to study interest rate elasticities of loan demand in microfinance and the impact of education on wages

efficiency bounds for missing data models with semiparametric restrictions this paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random mar coincides with that of a particular augmented moment condition problem the augmented system consists of the inverse probability weighted ipw original moment restriction and an additional conditional moment restriction which exhausts all other implications of the mar assumption the paper also investigates the value of additional semiparametric restrictions on the conditional expectation function cef of the original moment function given always observed covariates in the program evaluation context for example such restrictions are implied by semiparametric models for the potential outcome cefs given baseline covariates the efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem some implications of these results for estimation are briefly discussed

testing conditional independence via rosenblatt transforms this paper proposes new tests of conditional independence of two random variables given a single index involving an unknown finite dimensional parameter the tests employ rosenblatt transforms and are shown to be distribution free while retaining computational convenience some results from monte carlo simulations are presented and discussed

estimation of controlled direct effects when regression models adjust for mediators on the causal path from exposure to outcome the regression coefficient of exposure is commonly viewed as a measure of the direct exposure effect this interpretation can be misleading even with a randomly assigned exposure this is because adjustment for post exposure measurements introduces bias whenever their association with the outcome is confounded by more than just the exposure by the same token adjustment for such confounders stays problematic when these are themselves affected by the exposure robins accommodated this by introducing linear structural nested direct effect models with direct effect parameters that can be estimated by using inverse probability weighting by a conditional distribution of the mediator the resulting estimators are consistent but inefficient and can be extremely unstable when the mediator is absolutely continuous we develop direct effect estimators which are not only more efficient but also consistent under a less demanding model for a conditional expectation of the outcome we find that the one estimator which avoids inverse probability weighting altogether performs best this estimator is intuitive computationally straightforward and as demonstrated by simulation competes extremely well with ordinary least squares estimators in settings where standard regression is valid

generalized causal mediation analysis the goal of mediation analysis is to assess direct and indirect effects of a treatment or exposure on an outcome more generally we may be interested in the context of a causal model as characterized by a directed acyclic graph dag where mediation via a specific path from exposure to outcome may involve an arbitrary number of links or stages methods for estimating mediation or pathway effects are available for a continuous outcome and a continuous mediator related via a linear model while for a categorical outcome or categorical mediator methods are usually limited to two stage mediation we present a method applicable to multiple stages of mediation and mixed variable types using generalized linear models we define pathway effects using a potential outcomes framework and present a general formula that provides the effect of exposure through any specified pathway some pathway effects are nonidentifiable and their estimation requires an assumption regarding the correlation between counterfactuals we provide a sensitivity analysis to assess the impact of this assumption confidence intervals for pathway effect estimates are obtained via a bootstrap method the method is applied to a cohort study of dental caries in very low birth weight adolescents a simulation study demonstrates low bias of pathway effect estimators and close to nominal coverage rates of confidence intervals we also find low sensitivity to the counterfactual correlation in most scenarios

two step estimation in ratio of mediator probability weighted causal mediation analysis this study investigates appropriate estimation of estimator variability in the context of causal mediation analysis that employs propensity score based weighting such an analysis decomposes the total effect of a treatment on the outcome into an indirect effect transmitted through a focal mediator and a direct effect bypassing the mediator ratio of mediator probability weighting estimates these causal effects by adjusting for the confounding impact of a large number of pretreatment covariates through propensity score based weighting in step 1 a propensity score model is estimated in step 2 the causal effects of interest are estimated using weights derived from the prior step s regression coefficient estimates statistical inferences obtained from this 2 step estimation procedure are potentially problematic if the estimated standard errors of the causal effect estimates do not reflect the sampling uncertainty in the estimation of the weights this study extends to ratio of mediator probability weighting analysis a solution to the 2 step estimation problem by stacking the score functions from both steps we derive the asymptotic variance covariance matrix for the indirect effect and direct effect 2 step estimators provide simulation results and illustrate with an application study our simulation results indicate that the sampling uncertainty in the estimated weights should not be ignored the standard error estimation using the stacking procedure offers a viable alternative to bootstrap standard error estimation we discuss broad implications of this approach for causal analysis involving propensity score based weighting

semiparametric theory for causal mediation analysis efficiency bounds multiple robustness and sensitivity analysis whilst estimation of the marginal total causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences in recent years investigators have also become increasingly interested in mediation analysis specifically upon evaluating the total effect of the exposure investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure not through or through a mediator variable that occurs subsequently to the exposure and prior to the outcome although powerful semiparametric methodologies have been developed to analyze observational studies that produce double robust and highly efficient estimates of the marginal total causal effect similar methods for mediation analysis are currently lacking thus this paper develops a general semiparametric framework for obtaining inferences about so called marginal natural direct and indirect causal effects while appropriately accounting for a large number of pre exposure confounding factors for the exposure and the mediator variables our analytic framework is particularly appealing because it gives new insights on issues of efficiency and robustness in the context of mediation analysis in particular we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable

bubble size topology correlations in two dimensional foams derived from surface energy minimization we obtain the number fractions xi the average areas a i and the average perimeters p i of i sided bubbles in a two dimensional foam by minimizing the total surface energy and assuming a simple relation between p i and a i calculations for linear and weibull distributions of the square root of the bubble area yield large deviations particularly at small i from lewis s and desch s laws which linearly relate a i and p i respectively to i nevertheless we find good agreement with experimental results for xi p i and a i in foams

model averaging in semiparametric estimation of treatment effects choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects this paper proposes a data driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the att the proposed procedures minimize the estimated mse of the att estimator in a local asymptotic framework we formulate model averaging as a statistical decision problem in a limit experiment and derive an averaging scheme that is bayes optimal with respect to a given prior the averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of bayes asymptotic mse our monte carlo studies illustrate the size of the mse gains we apply the averaging procedure to evaluate the effect of a labor market program

bayesian estimation of the average treatment effect on the treated using inverse weighting we develop a bayesian approach to estimate the average treatment effect on the treated in the presence of confounding the approach builds on developments proposed by saarela et al in the context of marginal structural models using importance sampling weights to adjust for confounding and estimate a causal effect the bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in bayesian causal estimation relying on a joint likelihood we present results from simulation studies to estimate the average treatment effect on the treated evaluating the impact of sample size and the strength of confounding on estimation we illustrate our approach using the classic right heart catheterization data set and find a negative causal effect of the exposure on 30 day survival in accordance with previous analyses of these data we also apply our approach to the data set of the national center for health statistics birth data and obtain a negative effect of maternal smoking during pregnancy on birth weight

sharp sensitivity bounds for mediation under unmeasured mediator outcome confounding it is often of interest to decompose the total effect of an exposure into a component that acts on the outcome through some mediator and a component that acts independently through other pathways said another way we are interested in the direct and indirect effects of the exposure on the outcome even if the exposure is randomly assigned it is often infeasible to randomize the mediator leaving the mediator outcome confounding not fully controlled we develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured mediator outcome confounding

a variational approach to modeling and simulation of grain growth most technologically useful materials arise as polycrystalline microstructures composed of a myriad of small crystallites called grains separated by their interfaces called grain boundaries the orientations and arrangements of the grains and their network of boundaries are implicated in many properties across wide scales for example functional properties like conductivity in microprocessors and lifetime properties like fracture toughness in structures simulation is becoming an important tool for understanding both materials properties and their processing requirements here we offer a consistent variational approach to the mesoscale simulation of these systems subject to the mullins equation of curvature driven growth in a two dimensional setting the main objective is to provide a calibration for future two dimensional and three dimensional efforts we discuss several novel features of our approach which we anticipate will render it a flexible scalable and robust tool to aid in microstructural prediction simulation results offer compelling evidence of the predictability and robustness of statistical properties of large systems such as grain size distribution and texture that are of immediate interest in materials science

space time large deviations for interacting particle systems the asymptotic behavior of the space time empirical averages of several classes of interacting particle systems is studied here the authors prove that the empirical averages obey a process level large deviation principle whose rate function is given explicitly in the case of spin systems the authors establish some relevant properties of the rate function such as the correspondence between its minima and the invariant measures for the process finally for discrete time non ergodic systems the authors give some results on the critical behavior of the empirical averages

statistical assessment of mediational effects for logistic mediational models the concept of mediation has broad applications in medical health studies although the statistical assessment of a mediational effect under the normal assumption has been well established in linear structural equation models sem it has not been extended to the general case where normality is not a usual assumption in this paper we propose to extend the definition of mediational effects through causal inference the new definition is consistent with that in linear sem and does not rely on the assumption of normality here we focus our attention on the logistic mediation model where all variables involved are binary three approaches to the estimation of mediational effects delta method bootstrap and bayesian modelling via monte carlo simulation are investigated simulation studies are used to examine the behaviour of the three approaches measured by 95 per cent confidence interval ci coverage rate and root mean square error rmse criteria it was found that the bayesian method using a non informative prior outperformed both bootstrap and the delta methods particularly for small sample sizes case studies are presented to demonstrate the application of the proposed method to public health research using a nationally representative database extending the proposed method to other types of mediational model and to multiple mediators are also discussed

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

stable spins in the zero temperature spinodal decomposition of 2d potts models we present the results of zero temperature monte carlo simulations of the q state potts model on a square lattice with either four or eight neighbors and for the triangular lattice with six neighbors in agreement with previous works we observe that the domain growth process gets blocked for the nearest neighbor square lattice when q is large enough whereas for the eight neighbor square lattice and for the triangular lattice no blocking is observed our simulations indicate that the number of spins which never flipped from the beginning of the simulation up to time t follows a power law as a function of the energy even in the case of blocking the exponent of this power law varies from less than 1 2 for the ising case q 2 to 2 for q o0 and seems to be universal the effect of blocking on this exponent is invisible at least up to q 7

joint regression analysis of correlated data using gaussian copulas this article concerns a new joint modeling approach for correlated data analysis utilizing gaussian copulas we present a unified and flexible machinery to integrate separate one dimensional generalized linear models glms into a joint regression analysis of continuous discrete and mixed correlated outcomes this essentially leads to a multivariate analogue of the univariate glm theory and hence an efficiency gain in the estimation of regression coefficients the availability of joint probability models enables us to develop a full maximum likelihood inference numerical illustrations are focused on regression models for discrete correlated data including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes in the simulation studies the proposed copula based joint model is compared to the popular generalized estimating equations which is a moment based estimating equation method to join univariate glms two real world data examples are used in the illustration

universality in two dimensional cellular structures evolving by cell division and disappearance the dynamics of two dimensional cellular networks is written in terms of coupled population equations which describe how the population of s sided cells is affected by cell division and disappearance in these equations the effect of the rest of the foam on the disappearing or dividing cell is treated as a local mean field under not too restrictive conditions the equilibrium distribution p s of cells satisfies a linear difference equation of order two or higher the population equations are asymptotically integrable the asymptotic integrability implies a universal distribution p s approximately cs kzs for large values of s which is also the boltzmann distribution associated with the maximum entropy inference asymptotic integrability of the population equations is absent in a global mean field approximation the importance of short range topological information to control the evolution of foams is thus confirmed

methods for dealing with time dependent confounding longitudinal studies where data are repeatedly collected on subjects over a period are common in medical research when estimating the effect of a time varying treatment or exposure on an outcome of interest measured at a later time standard methods fail to give consistent estimators in the presence of time varying confounders if those confounders are themselves affected by the treatment robins and colleagues have proposed several alternative methods that provided certain assumptions hold avoid the problems associated with standard approaches they include the g computation formula inverse probability weighted estimation of marginal structural models and g estimation of structural nested models in this tutorial we give a description of each of these methods exploring the links and differences between them and the reasons for choosing one over the others in different settings

scaling laws and topological exponents in voronoi tessellations of intermittent point distributions voronoi tessellations of scale invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures as an example we analyse voronoi diagrams of intermittent particle distributions generated by a directed percolation process in 2 1 dimensions we observe that the average area of a cell increases much faster with the number of its neighbours than in natural cellular structures where lewis law predicts a linear behaviour we propose and numerically verify a universal scaling law that relates shape and size of the cells in scale invariant tessellations an exponent related to the topological properties of the tessellation is introduced and estimated numerically

non trivial exponents in coarsening phenomena abstract one of the simplest examples of stochastic automata is the glauber dynamics of ferromagnetic spin models such as ising or potts models at zero temperature if the initial condition is random one observes a pattern of growing domains with a characteristic size which increases with time like t 1 2 in this self similar regime the fraction of spins which never flip up to time t decreases like t where the exponent is non trivial and depends both on the number q of states of the potts model and on the dimension of space this exponent can be calculated exactly in one dimension similar non trivial exponents are also present in even simpler models of coarsening where the dynamical rule is deterministic

multiple robustness in factorized likelihood models we consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation independent factors we are interested in a finite dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions we investigate general structures conducive to the construction of so called multiply robust estimating functions whose computation requires postulating several dimension reducing models but which have mean zero at the true parameter value provided one of these models is correct