functional data clustering via piecewise constant nonparametric density estimation in this paper we present a novel way of analyzing and summarizing a collection of curves based on piecewise constant density estimation the curves are partitioned into clusters and the dimensions of the curves points are discretized into intervals the cross product of these univariate partitions forms a data grid of cells which represents a nonparametric estimator of the joint density of the curves and point dimensions the best model is selected using a bayesian model selection approach and retrieved using combinatorial optimization algorithms the proposed method requires no parameter setting and makes no assumption regarding the curves beyond functional data it can be applied to distributional data the practical interest of the approach for functional data and distributional data exploratory analysis is presented on two real world datasets

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

matching on the estimated propensity score propensity score matching estimators rosenbaum and rubin 1983 are widely used in evaluation research to estimate average treatment effects in this article we derive the large sample distribution of propensity score matching estimators our derivations take into account that the propensity score is itself estimated in a first step prior to matching we prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect ate and the average treatment effect on the treated atet the adjustment for the ate estimator is negative or zero in some special cases implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples however for the atet estimator the sign of the adjustment term depends on the data generating process and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small

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

nonparametric estimation of the mode of a distribution of random curves summary motivated by the need to develop meaningful empirical approximations to a typical data value we introduce methods for density and mode estimation when data are in the form of random curves our approach is based on finite dimensional approximations via generalized fourier expansions on an empirically chosen basis the mode estimation problem is reduced to a problem of kernel type multivariate estimation from vector data and is solved using a new recursive algorithm for finding the empirical mode the algorithm may be used as an aid to the identification of clusters in a set of data curves bootstrap methods are employed to select the bandwidth

robust confidence intervals for average treatment effects under limited overlap limited overlap between the covariate distributions of groups with different treatment assignments does not only make estimates of average treatment effects rather imprecise but can also lead to substantially distorted confidence intervals this paper argues that this is because the coverage error of traditional confidence intervals is driven by the number of observations in the areas of limited overlap some of these local sample sizes can be very small in applications up to the point that distributional approximations derived from classical asymptotic theory become unreliable building on this observation this paper constructs confidence intervals based on classical approaches to small sample inference the approach is easy to implement and has superior theoretical and practical properties relative to standard methods in empirically relevant settings

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

kernel based covariate functional balancing for observational studies covariate balance is often advocated for objective causal inference since it mimics randomization in observational data unlike methods that balance specific moments of covariates our proposal attains uniform approximate balance for covariate functions in a reproducing kernel hilbert space the corresponding infinite dimensional optimization problem is shown to have a finite dimensional representation in terms of an eigenvalue optimization problem large sample results are studied and numerical examples show that the proposed method achieves better balance with smaller sampling variability than existing methods

an alternative empirical likelihood method in missing response problems and causal inference missing responses are common problems in medical social and economic studies when responses are missing at random a complete case data analysis may result in biases a popular debias method is inverse probability weighting proposed by horvitz and thompson to improve efficiency robins et al proposed an augmented inverse probability weighting method the augmented inverse probability weighting estimator has a double robustness property and achieves the semiparametric efficiency lower bound when the regression model and propensity score model are both correctly specified in this paper we introduce an empirical likelihood based estimator as an alternative to qin and zhang 2007 our proposed estimator is also doubly robust and locally efficient simulation results show that the proposed estimator has better performance when the propensity score is correctly modeled moreover the proposed method can be applied in the estimation of average treatment effect in observational causal inferences finally we apply our method to an observational study of smoking using data from the cardiovascular outcomes in renal atherosclerotic lesions clinical trial copyright 2016 john wiley sons ltd

semiparametric regression analysis with missing response at random we develop inference tools in a semiparametric partially linear regression model with missing response data a class of estimators is defined that includes as special cases a semiparametric regression imputation estimator a marginal average estimator and a marginal propensity score weighted estimator we show that any of our class of estimators is asymptotically normal the three special estimators have the same asymptotic variance they achieve the semiparametric efficiency bound in the homoscedastic gaussian case we show that the jackknife method can be used to consistently estimate the asymptotic variance our model and estimators are defined with a view to avoid the curse of dimensionality which severely limits the applicability of existing methods the empirical likelihood method is developed it is shown that when missing responses are imputed using the semiparametric regression method the empirical log likelihood is asymptotically a scaled chi squared variable an adjusted empirical log likel

partial identification of functionals of the joint distribution of potential outcomes in this paper we present a systematic study of partial identification of two general classes of functionals of the joint distribution of two potential outcomes when a bivariate sample from the joint distribution is not available to the econometrician assuming the identification of the conditional marginal distributions of potential outcomes and the distribution of the covariate vector we show that the identified sets for functionals in both classes are intervals and provide conditions under which the identified sets point identify the true value of the functionals in addition we establish sufficient and necessary conditions for the covariate information to be informative in the sense of shrinking the identified sets we focus on the application of our general results to evaluating distributional treatment effects of a binary treatment in two commonly used frameworks in the literature for evaluating average treatment effects the selection on observables framework and a latent threshold crossing model we characterize the role of the propensity score in the selection on observables framework and the role of endogenous selection in the latent threshold crossing model examples of policy parameters that our results apply include the correlation coefficient between the potential outcomes many inequality measures of the distribution of treatment effects and median of the distribution of the individual treatment effect

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

formulating a mixed integer programming problem to improve solvability a standard formulation of a real world distribution problem could not be solved even for a good solution by a commercial mixed integer programming code however after reformulating it by reducing the number of 0 1 variables and tightening the linear programming relaxation an optimal solution could be found efficiently the purpose of this paper is to demonstrate with a real application the practical importance of the need for good formulations in solving mixed integer programming problems

defining probability density for a distribution of random functions the notion of probability density for a random function is not as straightforward as in finite dimensional cases while a probability density function generally does not exist for functional data we show that it is possible to develop the notion of density when functional data are considered in the space determined by the eigenfunctions of principal component analysis this leads to a transparent and meaningful surrogate for density defined in terms of the average value of the logarithms of the densities of the distributions of principal components for a given dimension this density approximation is estimable readily from data it accurately represents in a monotone way key features of small ball approximations to density our results on estimators of the densities of principal component scores are also of independent interest they reveal interesting shape differences that have not previously been considered the statistical implications of these results and properties are identified and discussed and practical ramifications are illustrated in numerical work

polytopes associated with symmetry handling this paper investigates a polyhedral approach to handle symmetries in mixed binary programs we study symretopes i e the convex hulls of all binary vectors that are lexicographically maximal in their orbit with respect to the symmetry group these polytopes turn out to be quite complex for practical use we therefore develop an integer programming formulation with ternary coefficients based on knapsack polytopes arising from a single lexicographic order enforcing inequality we show that for these polytopes the optimization as well as the separation problem of minimal cover inequalities can be solved in almost linear time we demonstrate the usefulness of this approach by computational experiments showing that it is competitive with state of the art methods and is considerably faster for specific problem classes

balancing covariates via propensity score weighting abstractcovariate balance is crucial for unconfounded descriptive or causal comparisons however lack of balance is common in observational studies this article considers weighting strategies for balancing covariates we define a general class of weights the balancing weights that balance the weighted distributions of the covariates between treatment groups these weights incorporate the propensity score to weight each group to an analyst selected target population this class unifies existing weighting methods including commonly used weights such as inverse probability weights as special cases general large sample results on nonparametric estimation based on these weights are derived we further propose a new weighting scheme the overlap weights in which each unit s weight is proportional to the probability of that unit being assigned to the opposite group the overlap weights are bounded and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing wei

a robust and efficient approach to causal inference based on sparse sufficient dimension reduction a fundamental assumption used in causal inference with observational data is that treatment assignment is ignorable given measured confounding variables this assumption of no missing confounders is plausible if a large number of baseline covariates are included in the analysis as we often have no prior knowledge of which variables can be important confounders thus estimation of treatment effects with a large number of covariates has received considerable attention in recent years most existing methods require specifying certain parametric models involving the outcome treatment and confounding variables and employ a variable selection procedure to identify confounders however selection of a proper set of confounders depends on correct specification of the working models the bias due to model misspecification and incorrect selection of confounding variables can yield misleading results we propose a robust and efficient approach for inference about the average treatment effect via a flexible modeling strategy incorporating penalized variable selection specifically we consider an estimator constructed based on an efficient influence function that involves a propensity score and an outcome regression we then propose a new sparse sufficient dimension reduction method to estimate these two functions without making restrictive parametric modeling assumptions the proposed estimator of the average treatment effect is asymptotically normal and semiparametrically efficient without the need for variable selection consistency the proposed methods are illustrated via simulation studies and a biomedical application

improving discrete model representations via symmetry considerations in this paper we focus on a useful modeling concept that is frequently ignored while formu lating discrete optimization problems very often there exists a natural symmetry inherent in the problem itself that if propagated to the model can hopelessly mire a branch and bound solver by burdening it to explore and eliminate such alternative symmetric solutions we discuss three applications where such a symmetry arises a telecommunications network design problem a noise pollution problem and a machine procurement and operation problem for each case we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability while using a popular modern day commercial branch and cut software cplex 6 5

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

gmm redundancy results for general missing data problems we consider questions of efficiency and redundancy in the gmm estimation problem in which we have two sets of moment conditions where two sets of parameters enter into one set of moment conditions while only one set of parameters enters into the other we then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest and the second set of moment conditions is for the selection process we use these results to explain the counterintuitive result in the literature that under an ignorability assumption that justifies gmm with weighted moment conditions weighting using estimated probabilities of selection is better than weighting using the true probabilities we also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid and we show that when weighting is not needed for consistency it is also not useful for efficiency

optimal allocation of surgery blocks to operating rooms under uncertainty the allocation of surgeries to operating rooms ors is a challenging combinatorial optimization problem there is also significant uncertainty in the duration of surgical procedures which further complicates assignment decisions in this paper we present stochastic optimization models for the assignment of surgeries to ors on a given day of surgery the objective includes a fixed cost of opening ors and a variable cost of overtime relative to a fixed length of day we describe two types of models the first is a two stage stochastic linear program with binary decisions in the first stage and simple recourse in the second stage the second is its robust counterpart in which the objective is to minimize the maximum cost associated with an uncertainty set for surgery durations we describe the mathematical models bounds on the optimal solution and solution methodologies including an easy to implement heuristic numerical experiments based on real data from a large health care provider are used to contrast the results for the two models and illustrate the potential for impact in practice based on our numerical experimentation we find that a fast and easy to implement heuristic works fairly well on average across many instances we also find that the robust method performs approximately as well as the heuristic is much faster than solving the stochastic recourse model and has the benefit of limiting the worst case outcome of the recourse problem

endogenous selection or treatment model estimation in a sample selection or treatment effects model common unobservables may affect both the outcome and the probability of selection in unknown ways this paper shows that the distribution function of potential outcomes conditional on covariates can be identified given an observed variable v that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes selection model estimators based on this identification are provided which take the form of simple weighted averages gmm or two stage least squares these estimators permit endogenous and mismeasured regressors empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model

reformulations in mathematical programming automatic symmetry detection and exploitation if a mathematical program has many symmetric optima solving it via branch and bound techniques often yields search trees of disproportionate sizes thus finding and exploiting symmetries is an important task we propose a method for automatically finding the formulation group of any given mixed integer nonlinear program and for reformulating the problem by means of static symmetry breaking constraints the reformulated problem which is likely to have fewer symmetric optima can then be solved via standard branch and bound codes such as cplex for linear programs and couenne for nonlinear programs our computational results include formulation group tables for the miplib3 miplib2003 globallib and minlplib instance libraries and solution tables for some instances in the aforementioned libraries

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

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

an accelerated branch and price algorithm for multiple runway aircraft sequencing problems abstract this paper presents an effective branch and price b p algorithm for multiple runway aircraft sequencing problems this approach improves the tractability of the problem by several orders of magnitude when compared with solving a classical 0 1 mixed integer formulation over a set of computationally challenging instances central to the computational efficacy of the b p algorithm is solving the column generation subproblem as an elementary shortest path problem with aircraft time windows and non triangular separation times using an enhanced dynamic programming procedure we underscore in our computational study the algorithmic features that contribute in our experience to accelerating the proposed dynamic programming procedure and hence the overall b p algorithm

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

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

efficient semiparametric estimation of quantile treatment effects this paper develops estimators for quantile treatment effects under the identifying restriction that selection to treatment is based on observable characteristics identification is achieved without requiring computation of the conditional quantiles of the potential outcomes instead the identification results for the marginal quantiles lead to an estimation procedure for the quantile treatment effect parameters that has two steps nonparametric estimation of the propensity score and computation of the difference between the solutions of two separate minimization problems root n consistency asymptotic normality and achievement of the semiparametric efficiency bound are shown for that estimator a consistent estimation procedure for the variance is also presented finally the method developed here is applied to evaluation of a job training program and to a monte carlo exercise results from the empirical application indicate that the method works relatively well even for a data set with limited overlap between treated and controls in the support of covariates the monte carlo study shows that for a relatively small sample size the method produces estimates with good precision and low bias especially for middle quantiles

estimation of mean response via the effective balancing score we introduce effective balancing scores for estimation of the mean response under a missing at random mechanism unlike conventional balancing scores the effective balancing scores are constructed via dimension reduction free of model specification three types of effective balancing scores are introduced those that carry the covariate information about the missingness the response or both they lead to consistent estimation with little or no loss in efficiency compared to existing estimators the effective balancing score based estimator relieves the burden of model specification and is the most robust it is a near automatic procedure which is most appealing when high dimensional covariates are involved we investigate both the asymptotic and the numerical properties and demonstrate the proposed method in a study on human immunodeficiency virus disease

irregular identification support conditions and inverse weight estimation in weighted moment condition models we show a subtle link between identification and estimability that limits the practical usefulness of estimators based on these models in particular if it is necessary for point identification that the weights take arbitrarily large values then the parameter of interest though point identified cannot be estimated at the regular parametric rate and is said to be irregularly identified this rate depends on relative tail conditions and can be as slow in some examples as n 1 4 this nonstandard rate of convergence can lead to numerical instability and or large standard errors we examine two weighted model examples i the binary response model under mean restriction introduced by lewbel 1997 and further generalized to cover endogeneity and selection where the estimator in this class of models is weighted by the density of a special regressor and ii the treatment effect model under exogenous selection rosenbaum and rubin 1983 where the resulting estimator of the average treatment effect is one that is weighted by a variant of the propensity score without strong relative support conditions these models similar to well known identified at infinity models lead to estimators that converge at slower than parametric rate since essentially to ensure point identification one requires some variables to take values on sets with arbitrarily small probabilities or thin sets for the two models above we derive some rates of convergence and propose that one conducts inference using rate adaptive procedures that are analogous to andrews and schafgans 1998 for the sample selection model

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

ilp approaches to the blockmodel problem blockmodelling is a method for identifying structural similarities or equivalences between elements which has applications in a variety of contexts including multiattribute performance assessment one criterion for forming blocks results in a difficult non linear integer programme we give several integer linear programming formulations of this problem and provide comparative computational results we show that methods of reducing symmetry proposed by sherali and smith are not effective in this case and propose an iterative approach in which the size of the problem is reduced

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 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

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 sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

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

three stage semi parametric inference control variables and differentiability abstract we show the usefulness of the path derivative calculations that were introduced in econometrics by newey 1994 for multi step semi parametric estimators these estimators estimate a finite dimensional parameter using moment conditions that depend on nonparametric regressions on observed and estimated regressors that are estimated in the second and first step of the estimation procedure respectively our earlier paper showed that newey s calculations can be extended to three step estimators in the current paper we consider the control variable cv estimator and related statistics in semi parametric econometric models with non separable errors and regressors that are correlated with these errors non separable econometric models with endogenous regressors are often identified by average moment restrictions that average over control variables and these control variables are estimated in a first stage by non parametric regression we study aspects of inference for such estimators where we focus on a finite dimensional parameter vector or statistic the asymptotic distribution and a closed form expression for the asymptotic variance of the cv estimator were not available until now our path derivative calculations are much simpler than the derivation of the asymptotic distribution by a stochastic expansion that is particularly complicated for multi step semi parametric estimators we also consider just and overidentification of the parameters and we propose a diagnostic test for overidentifying restrictions in models with non separable errors and endogenous regressors finally the path derivative calculation breaks down if the moment condition is not differentiable in an example we show that non differentiability is associated with irregular behavior of the estimator

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

propensity score matching and subclassification in observational studies with multi level treatments in this article we develop new methods for estimating average treatment effects in observational studies in settings with more than two treatment levels assuming unconfoundedness given pretreatment variables we emphasize propensity score subclassification and matching methods which have been among the most popular methods in the binary treatment literature whereas the literature has suggested that these particular propensity based methods do not naturally extend to the multi level treatment case we show using the concept of weak unconfoundedness and the notion of the generalized propensity score that adjusting for a scalar function of the pretreatment variables removes all biases associated with observed pretreatment variables we apply the proposed methods to an analysis of the effect of treatments for fibromyalgia we also carry out a simulation study to assess the finite sample performance of the methods relative to previously proposed methods

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

estimation of the effect of interventions that modify the received treatment motivated by a study of surgical operating time and post operative outcomes for lung cancer we consider the estimation of causal effects of continuous point exposure treatments to investigate causality the standard paradigm postulates a series of treatment specific counterfactual outcomes and establishes conditions under which we may learn about them from observational study data while many choices are possible causal effects are typically defined in terms of variation of the mean of counterfactual outcomes in hypothetical worlds in which specific treatment strategies are applied to all individuals for example one might compare two worlds one where each individual receives some specific dose and a second where each individual receives some other dose for our motivating study defining causal effects in this way corresponds to hypothetical interventions that could not conceivably be implemented in the real world in this work we consider an alternative complimentary framework that investigates variation in the mean of counterfactual outcomes under hypothetical treatment strategies where each individual receives a treatment dose corresponding to that actually received but modified in some pre specified way quantification of this variation is defined in terms of contrasts for specific interventions as well as in terms of the parameters of a new class of marginal structural mean models within this framework we propose three estimators an outcome regression estimator an inverse probability of treatment weighted estimator and a doubly robust estimator we illustrate the methods with an analysis of the motivating data copyright 2013 john wiley sons ltd

kernel smoothing approaches to nonparametric item characteristic curve estimation the option characteristic curve the relation between ability and probability of choosing a particular option for a test item can be estimated by nonparametric smoothing techniques what is smoothed is the relation between some function of estimated examinee ability rankings and the binary variable indicating whether or not the option was chosen this paper explores the use of kernel smoothing which is particularly well suited to this application examples show that with some help from the fast fourier transform estimates can be computed about 500 times as rapidly as when using commonly used parametric approaches such as maximum marginal likelihood estimation using the three parameter logistic distribution simulations suggest that there is no loss of efficiency even when the population curves are three parameter logistic the approach lends itself to several interesting extensions

optimal placement of add drop multiplexers heuristic and exact algorithms we study a problem that has arisen recently in the design of telecommunications transmission networks at france telecom given a set of centers in a city or conglomeration linked together on a ring architecture given the expected demands between the centers and an essentially unlimited availability of rings of fixed capacity on the network assign demand pairs and corresponding add drop multiplexers to the rings so as to satisfy the demands and minimize the number of costly multiplexers installed heuristics based on simulated annealing have been developed for the basic problem and several variants france telecom is particularly interested in validating the effectiveness of the heuristics an exact algorithm based on integer column generation is shown to provide tight performance guarantees and in most cases to give provable minimum cost solutions column generation is used even though the subproblems are strongly np hard and are solved by standard mixed integer programming software in addition the master problems involve both integer columns and integer variables whereas these are 0 1 in most reported applications

a note on a symmetrical set covering problem the lottery problem in a lottery n numbers are drawn from a set of m numbers on a lottery ticket we fill out n numbers consider the following problem what is the minimum number of tickets so that there is at least one ticket with at least p matching numbers we provide a set covering formulation for this problem and characterize its lp solution the existence of many symmetrical alternative solutions makes this a very difficult problem to solve as our computational results indicate

enhanced model formulations for optimal facility layout this paper presents an improved mixed integer programming mip model and effective solution strategies for the facility layout problem and is motivated by the work of meller et al 1999 this class of problems seeks to determine a least cost layout of departments having various size and area requirements within a rectangular building and it is challenging even for small instances the difficulty arises from the disjunctive constraints that prevent departmental overlaps and the nonlinear area constraints for each department which existing models have failed to approximate with adequate accuracy we develop several modeling and algorithmic enhancements that are demonstrated to produce more accurate solutions while also decreasing the solution effort required we begin by deriving a novel polyhedral outer approximation scheme that can provide as accurate a representation of the area requirements as desired we also design alternative methods for reducing problem symmetry evaluate the performance of several classes of valid inequalities explore the construction of partial convex hull representations for the disjunctive constraints and investigate judicious branching variable selection priority schemes the results indicate asubstantial increase in the accuracy of the layout produced while at the same time providing adramatic reduction in computational effort in particular three previously unsolved test problems from the literature for which meller et al s algorithm terminated prematurely after 24 cpu hours of computation on a sun ultra 2 workstation with 390 mb ram with respective optimality gaps of 10 14 26 45 and 40 have been solved to exact optimality with reasonable effort using our proposed approach

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

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

doubly robust inference for targeted minimum loss based estimation in randomized trials with missing outcome data missing outcome data is a crucial threat to the validity of treatment effect estimates from randomized trials the outcome distributions of participants with missing and observed data are often different which increases bias causal inference methods may aid in reducing the bias and improving efficiency by incorporating baseline variables into the analysis in particular doubly robust estimators incorporate 2 nuisance parameters the outcome regression and the missingness mechanism ie the probability of missingness conditional on treatment assignment and baseline variables to adjust for differences in the observed and unobserved groups that can be explained by observed covariates to consistently estimate the treatment effect one of these nuisance parameters must be consistently estimated traditionally nuisance parameters are estimated using parametric models which often precludes consistency particularly in moderate to high dimensions recent research on missing data has focused on data adaptive estimation to help achieve consistency but the large sample properties of such methods are poorly understood in this article we discuss a doubly robust estimator that is consistent and asymptotically normal under data adaptive estimation of the nuisance parameters we provide a formula for an asymptotically exact confidence interval under minimal assumptions we show that our proposed estimator has smaller finite sample bias compared to standard doubly robust estimators we present a simulation study demonstrating the enhanced performance of our estimators in terms of bias efficiency and coverage of the confidence intervals we present the results of an illustrative example a randomized double blind phase 2 3 trial of antiretroviral therapy in hiv infected persons

asymptotic variance of semiparametric estimators with generated regressors we study the asymptotic distribution of three step estimators of a finite dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step the first step estimator is either parametric or nonparametric using newey s 1994 path derivative method we derive the contribution of the first step estimator to the influence function in this derivation it is important to account for the dual role that the first step estimator plays in the second step nonparametric regression that is that of conditioning variable and that of argument

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

joint sufficient dimension reduction and estimation of conditional and average treatment effects the estimation of treatment effects based on observational data usually involves multiple confounders and dimension reduction is often desirable and sometimes inevitable we first clarify the definition of a central subspace that is relevant for the efficient estimation of average treatment effects a criterion is then proposed to simultaneously estimate the structural dimension the basis matrix of the joint central subspace and the optimal bandwidth for estimating the conditional treatment effects the method can easily be implemented by forward selection semiparametric efficient estimation of average treatment effects can be achieved by averaging the conditional treatment effects with a different data adaptive bandwidth to ensure optimal undersmoothing asymptotic properties of the estimated joint central subspace and the corresponding estimator of average treatment effects are studied the proposed methods are applied to a nutritional study where the covariate dimension is reduced from 11 to an effective dimension of one

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

semiparametric models with single index nuisance parameters abstract in many semiparametric models the parameter of interest is identified through conditional expectations where the conditioning variable involves a single index that is estimated in the first step among the examples are sample selection models and propensity score matching estimators when the first step estimator follows cube root asymptotics no method of analyzing the asymptotic variance of the second step estimator exists in the literature this paper provides nontrivial sufficient conditions under which the asymptotic variance is not affected by the first step single index estimator regardless of whether it is root n or cube root consistent the finding opens a way to simple inference procedures in these models results from monte carlo simulations show that the procedures perform well in finite samples

dealing with limited overlap in estimation of average treatment effects summary estimation of average treatment effects under unconfounded or ignorable treatment assignment is often hampered by lack of overlap in the covariate distributions between treatment groups this lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification in such cases researchers have often used ad hoc methods for trimming the sample we develop a systematic approach to addressing lack of overlap we characterize optimal subsamples for which the average treatment effect can be estimated most precisely under some conditions the optimal selection rules depend solely on the propensity score for a wide range of distributions a good approximation to the optimal rule is provided by the simple rule of thumb to discard all units with estimated propensity scores outside the range 0 1 0 9

dummy endogenous variables in weakly separable models in this paper we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term the model is not required to be strictly increasing in the error term and the class of models considered includes limited dependent variable models such as discrete choice models conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions

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

efficient local iv estimation of an empirical auction model abstract in this paper we examine semiparametric efficiency bounds and efficient estimators for the case of a linear local instrument variable liv model under the assumptions studied in abadie et al 2002 we apply the semiparametrically efficient estimation method to analyze the relation between bid dispersion and early bidding in an online auction dataset which is collected from a natural experiment conducted in nekipelov 2007 the results confirm the theoretical findings developed in nekipelov 2007 the semiparametric efficient estimation procedure substantially improves the statistical significance of the effect of jump bidding on bid dispersion

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

modified orbital branching for structured symmetry with an application to unit commitment the past decade has seen advances in general methods for symmetry breaking in mixed integer linear programming these methods are advantageous for general problems with general symmetry groups some important classes of mixed integer linear programming problems such as bin packing and graph coloring contain highly structured symmetry groups this observation has motivated the development of problem specific techniques in this paper we show how to strengthen orbital branching in order to exploit special structures in a problem s symmetry group the proposed technique to which we refer as modified orbital branching is able to solve problems with structured symmetry groups more efficiently one class of problems for which this technique is effective is when the solution variables can be expressed as 0 1 matrices where the problem s symmetry group contains all permutations of the columns we use the unit commitment problem an important problem in power systems to demonstrate the strength of modified orbital branching

nonparametric regression with nonparametrically generated covariates we analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable but have be estimated from data in a preliminary step these so called generated covariates appear in numerous applications including two stage nonparametric regression estimation of simultaneous equation models or censored regression models yet so far there seems to be no general theory for their impact on the final estimator s statistical properties our paper provides such results we derive a stochastic expansion that characterizes the influence of the generation step on the final estimator and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates

partial distributional policy effects in this paper we propose a method to evaluate the effect of a counterfactual change in the unconditional distribution of a single covariate on the unconditional distribution of an outcome variable of interest both fixed and infinitesimal changes are considered we show that such effects are point identified under general conditions if the covariate affected by the counterfactual change is continuously distributed but are typically only partially identified if its distribution is discrete for the latter case we derive informa tive bounds making use of the available information we also discuss estimation and inference

efficient propensity score regression estimators of multivalued treatment effects for the treated abstract when a multivalued treatment is randomly assigned conditional on observables valid causal comparisons for a subpopulation treated at a particular treatment level require two propensity scores one for the treated level and one for the counterfactual level we contribute efficient propensity score regression estimators to a class of treatment effects for the treated under the cases when the propensity scores are unknown and when they are known our efficient estimator matches on a normalized propensity score that combines the true propensity score and the nonparametric estimate our asymptotic theory takes into account that the propensity scores are nonparametrically or parametrically estimated as generated regressors

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

exploiting orbits in symmetric ilp this paper describes components of a branch and cut algorithm for solving integer linear programs having a large symmetry group it describes an isomorphism pruning algorithm and variable setting procedures using orbits of the symmetry group pruning and orbit computations are performed by backtracking procedures using a schreier sims table for representing the symmetry group applications to hard set covering problems generation of covering designs and error correcting codes are given

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

the impact of distribution system characteristics on computational tractability mathematical programming models that seek optimal design and operational plans for distribution systems can be computationally intractable this paper examines the extent to which distribution configuration and demand characteristics affect the ease of obtaining an optimal solution problem characteristics which are reflected in a model by the parameter values can render the model for one distribution scenario to be computationally intractable and that for another to yield an optimal solution easily we introduce echelon flow based valid inequalities and use them to explicate the extent to which problem characteristics impact computational tractability

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

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

empirical likelihood based inference in missing response problems and its application in observational studies summary the problem of missing response data is ubiquitous in medical and social science studies in the case of responses that are missing at random depending on some covariate information analyses focused only on the complete data may lead to biased results various debias methods have been extensively studied in the literature particularly the weighting method that was motivated by horvitz and thompson s estimators to improve efficiency robins rotnitzky and zhao proposed augmented estimating equations based on corrected complete case analyses a nice feature of the augmented method is its double robustness i e the estimator that is derived from the augmented method is asymptotically unbiased if either the underlying missing data mechanism or the underlying regression function is correctly specified furthermore the augmented estimator can achieve full efficiency if both the missing data mechanism and the regression function are correctly specified in general however it is very difficult to specify the regression function correctly especially when the dimension of covariates is high this is the so called curse of dimensionality problem the augmented estimator has much lower efficiency if the working regression model is not close to the true regression model in this paper the empirical likelihood method is employed to seek a constrained empirical likelihood estimation of mean response with the assumption that responses are missing at random the empirical likelihood based estimators enjoy the double robustness property moreover it is possible that the empirical likelihood based inference can produce asymptotically unbiased and efficient estimators even if the true regression function is not completely known simulation results indicate that the empirical likelihood based estimators are very robust to a misspecification of the propensity score and dominate other competitors in the sense of having smaller mean square errors methods that are developed in this paper have a nice application in observational causal inferences the propensity score is used to adjust for differences in pretreatment variables in the estimation of average treatment effects

mann whitney test with adjustments to pretreatment variables for missing values and observational study the conventional wilcoxon mann whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies this is because the missingness of the outcomes or the participation in the treatments may depend on certain pre treatment variables we propose an approach to adjust the mann whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre treatment variables we also propose semiparametric extensions of the adjusted mann whitney test which leads to dimension reduction for high dimensional covariate a novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach