semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

marginal longitudinal nonparametric regression locality and efficiency of spline and kernel methods we consider nonparametric regression in a longitudinal marginal model of generalized estimating equation gee type with a time varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large in such models the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations two methods of estimating the nonparametric function can be considered kernel methods and spline methods recently surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent that is working independence in the gee jargon as seen through equivalent kernel results in univariate independent data problems splines and kernels have similar behavior smoothing splines are equivalent to kernel regression with a s

temporal process regression summary we consider regression for response and covariates which are temporal processes observed over intervals a functional generalised linear model is proposed which includes extensions of standard models in multi state survival analysis simple nonparametric esti mators of time indexed parameters are developed using working independence estimating equations and are shown to be uniformly consistent and to converge weakly to gaussian processes the procedure does not require smoothing or a markov assumption unlike approaches based on transition intensities the usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy the estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters providing novel goodness of fit tests the methodology s practical utility is illustrated in a data analysis

the foundations of factor analysis summary a new approach to factor analysis and related latent variable methods is proposed which is based on data reduction using the idea of bayesian sufficiency considerations of symmetry invariance and independence are used to determine an appropriate family of models the results are expressed in terms of linear functions of the manifest variables after the manner of principal components analysis the approach justifies some of the practices based on the normal theory factor model and lays a foundation for the treatment of nonnormal including categorical variables 1 background factor analysis is a widely used statistical technique but its theoretical foundations are somewhat obscure and subject to dispute it is one of a family of multivariate methods which also includes latent structure and latent trait analysis the common feature of the models underlying these methods is that the observed random variables are assumed to depend on latent that is unobserved random variables there is sometimes debate about whether these latent variables are real in any sense but they can be viewed simply as constructs designed to simplify and summarize the complex web of interrelated variables with which nature confronts us by expressing these relationships in terms of a small number of latent variables or factors the models effect a reduction in dimensionality which aids comprehension an early theoretical account of the subject is by anderson rubin 1956 and more recent and comprehensive treatments are provided by lawley maxwell 1971 and harman 1968 the present paper is an attempt to provide a coherent framework within which existing methodology can be evaluated and a base from which new methods can be developed our approach is to start from a very general statement of the problem in terms of the distributions of the random variables involved and then to invoke ideas of symmetry invariance and conditional independence to determine the class of models that it is reasonable to consider this not only exhibits the unity of the various models already in existence but resolves many of the ambiguities and obscurities with which the subject has been bedevilled an early approach on these lines is given by anderson 1959 and was recognized by birnbaum in his contribution to lord novick 1968 the same line was followed by bartholomew 1980 in spite of this the practical implications do not seem to have been made fully explicit or generally recognized

diffusive limit of a tagged particle in asymmetric simple exclusion processes invariance principles are proved under diffusive scaling for the centered position of a tagged particle in the simple exclusion process with asymmetric nonzero drift jump probabilities in dimensions d 3 the method of proof is by martingale techniques which rely on the fact that symmetric random walks are transient in high dimensions c 2000 john wiley sons inc

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

integral formulas of the hilbert poincare bertrand schwarz and poisson type for the β analytic function theory abstract in the present work we obtain some analogues of the hilbert formulas on the unit circle and on the upper half plane for the theory of solutions of a special case of the beltrami equation in c to be referred as analytic functions furthermore a poincare bertrand formula related to the cauchy singular integral over a closed jordan curve is derived and it is used to derive the corresponding schwarz and poisson formulas

einstein relation for reversible diffusions in a random environment we consider reversible diffusions in a random environment and prove the einstein relation for this model it says that the derivative at 0 of the effective velocity under an additional local drift equals the diffusivity of the model without drift the einstein relation is conjectured to hold for a variety of models but so far it has only been proved in particular cases our proof makes use of homogenization arguments the girsanov transform and a refinement of the regeneration times introduced by shen 2011 wiley periodicals inc

nonparametric estimation of a multivariate distribution in the presence of censoring summary this paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right censored a distinction is made between what we term homogeneous and heterogeneous censoring it is shown how a multivariate empirical survivor function must be constructed in order to be considered a nonparametric maximum likelihood estimate of the underlying survivor function a closed form solution similar to the product limit estimate of kaplan and meier is possible with homogeneous censoring but an iterative method such as the em algorithm is required with heterogeneous censoring an example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables this anomaly is shown to disappear if

local dependence functions for some families of bivariate distributions and total positivity the purpose of this paper is to investigate a very useful application of a certain local dependence function c f x y which was considered recently by holland and wang 20 an interesting property of c f x y is that the underlying joint density f x y is tp 2 that is totally positive of order 2 if and only if c f x y 0 this gives an elegant way to investigate the tp 2 property of any bivariate distribution for the saramanov family the ali mikhail haq family of bivariate distributions and the family of bivariate elliptical distributions we derive the local dependence function and obtain conditions for f x y to be tp 2 these families are quite rich and include many other large classes of bivariate distributions as their special cases similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with pareto conditionals

poincare bertrand formula on a piecewise liapunov curve in two dimensional abstract the poincare bertrand formula for interchanging the order of integration in singular integral operators is generalized to the case of quaternionic singular integrals on a piecewise liapunov curve in two dimensional

practical issues in using generalized estimating equations for inference on transitions in longitudinal data what is being estimated generalized estimating equations gees are commonly used to estimate transition models when the markov assumption does not hold but first order transition probabilities are still of interest the transition inference is sensitive to the choice of working correlation in this paper we consider a random process transition model as the true underlying data generating mechanism which characterizes subject heterogeneity and complex dependence structure of the outcome process in a very flexible way we formally define two types of transition probabilities at the population level naive transition probabilities that average across all the transitions and population average transition probabilities that average the subject specific transition probabilities through asymptotic bias calculations and finite sample simulations we demonstrate that the unstructured working correlation provides unbiased estimators of the population average transition probabilities while the independence working correlation provides unbiased estimators of the naive transition probabilities for population average transition estimation we demonstrate that the sandwich estimator fails for unstructured gee and recommend the use of either jackknife or bootstrap variance estimates the proposed method is motivated by and applied to the next generation health study where the interest is in estimating the population average transition probabilities of alcohol use in adolescents

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

a functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error summary covariate measurement error and missing responses are typical features in longitudinal data analysis there has been extensive research on either covariate measurement error or missing responses but relatively little work has been done to address both simultaneously in this paper we propose a simple method for the marginal analysis of longitudinal data with time varying covariates some of which are measured with error while the response is subject to missingness our method has a number of appealing properties assumptions on the model are minimal with none needed about the distribution of the mismeasured covariate implementation is straightforward and its applicability is broad we provide both theoretical justification and numerical results

marginal mark regression analysis of recurrent marked point process data summary longitudinal studies typically collect information on the timing of key clinical events and on specific characteristics that describe those events random variables that measure qualitative or quantitative aspects associated with the occurrence of an event are known as marks recurrent marked point process data consist of possibly recurrent events with the mark and possibly exposure measured if and only if an event occurs analysis choices depend on which aspect of the data is of primary scientific interest first factors that influence the occurrence or timing of the event may be characterized using recurrent event analysis methods second if there is more than one event per subject then the association between exposure and the mark may be quantified using repeated measures regression methods we detail assumptions required of any time dependent exposure process and the event time process to ensure that linear or generalized linear mixed models and generalized estimating equations provide valid estimates we provide theoretical and empirical evidence that if these conditions are not satisfied then an independence estimating equation should be used for consistent estimation of association we conclude with the recommendation that analysts carefully explore both the exposure and event time processes prior to implementing a repeated measures analysis of recurrent marked point process data

pairwise dependence diagnostics for clustered failure time data frailty and copula models specify a parametric dependence structure for multivariate failure time data estimation of some joint quantities can be highly sensitive to the assumed parametric form and hence model fit is an important issue this paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models the approach is based on the cumulative sum of residuals that are calculated in bivariate time the residuals reflect the difference between the observed and expected bivariate association structures the proposed model checking process is interpretable with a limiting distribution which can be approximated using the bootstrap simulations and a data example illustrate the practical application of the method

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

modeling partly conditional means with longitudinal data abstract we propose a general modeling approach to longitudinal data that is a hybrid of the marginal regression models of zeger and liang and of the classical transition models such as used in time series analyses rather than conditioning at time t only on covariate values as is typical with the marginal approach or on the entire history of the process up to t as is typical with the transition model approach we suggest models that condition on a subset of the process history estimation proceeds using generalized estimating equation methodology but with the restriction that the working covariance matrix is diagonal the proposed regression models share common features with cox regression models for failure time data in that they are composed of a nuisance baseline function of time and a simple parametric function of the covariates two illustrative examples are presented

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates abstract recurrent event time data are common in medical research examples include infections in aids patients and seizures in epilepsy patients in this context as well as in the more usual context of a single failure time variable time dependent covariates are frequently of interest we suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time dependent covariate is of interest estimators of these functions are provided along with two sample test statistics a new approach to regression modeling of these data is suggested and contrasted with existing methods our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual this is in line with the currently popular generalized estimating equation approach to longitudinal data if the nature of such associations is known or is of particular interest then alternative methods may be appropriate

partly conditional estimation of the effect of a time dependent factor in the presence of dependent censoring we propose semiparametric methods for estimating the effect of a time dependent covariate on treatment free survival the data structure of interest consists of a longitudinal sequence of measurements and a potentially censored survival time the factor of interest is time dependent treatment free survival is of interest and is dependently censored by the receipt of treatment patients may be removed from consideration for treatment temporarily or permanently the proposed methods combine landmark analysis and partly conditional hazard regression a set of calendar time cross sections is specified and survival time from cross section date is modeled through weighted cox regression the assumed model for death is marginal in the sense that time varying covariates are taken as fixed at each landmark with the mortality hazard function implicitly averaging across future covariate trajectories dependent censoring is overcome by a variant of inverse probability of censoring weighting ipcw the proposed estimators are shown to be consistent and asymptotically normal with consistent covariance estimators provided simulation studies reveal that the proposed estimation procedures are appropriate for practical use we apply the proposed methods to pre transplant mortality among end stage liver disease esld patients

semiparametric and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

functional association models for multivariate survival processes we consider multivariate temporal processes that are continuously observed within overlapping time windows the intended application is in censored multistate and multivariate survival settings where point processes are continuously observed these data differ from other functional data like longitudinal data which are discretely observed at irregular times existing functional approaches to survival processes use intensity models which require smoothing and depend critically on the choice of smoothing parameters similarly to discretely observed data in this article we study functional mean and association regression models for the point processes with unspecified time varying coefficients the continuous observation scheme is exploited the coefficients may be estimated nonparametrically by extending generalized estimating equations to continuously observed data the estimators automatically converge at the parametric rate without smoothing unlike with discretely observed data uniform consistenc

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

semiparametric regression for clustered data using generalized estimating equations we consider estimation in a semiparametric generalized linear model for clustered data using estimating equations our results apply to the case where the number of observations per cluster is finite whereas the number of clusters is large the mean of the outcome variable is of the form g xt t where g is a link function x and t are covariates is an unknown parameter vector and t is an unknown smooth function kernel estimating equations proposed previously in the literature are used to estimate the infinite dimensional nonparametric function t and a profile based estimating equation is used to estimate the finite dimensional parameter vector we show that for clustered data this conventional profile kernel method often fails to yield a n consistent estimator of along with appropriate inference unless working independence is assumed or t is artificially undersmoothed in which case asymptotic inference is possible to gain insight into these results we derive the se

on the hilbert operator and the hilbert formulas on the unit sphere for the time harmonic maxwell equations in this work we establish some analogues of the hilbert formulas on the unit sphere for the theory of time harmonic monochromatic electromagnetic fields our formulas relate one of the components of the limit value of a time harmonic electromagnetic field in the unit ball to the rest of components the obtained results are based on the close relation between time harmonic solutions of the maxwell equations and the three dimensional hyperholomorphic function theory hilbert formulas for hyperholomorphic function theory for being a complex number are also obtained such formulas relate a pair of components of the boundary value of an hyperholomorphic function in the unit ball to the other pair of components in an analogy with what happens in the case of the theory of functions of one complex variable

partly functional temporal process regression with semiparametric profile estimating functions summary marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models recent work on fully functional temporal process regression tpr offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying the existing esti mation procedure however prevents successive goodness of fit test for covariate coefficients in comparing a sequence of nested models this article proposes a partly functional tpr model in the line of marginal mean models some covari ate effects are time independent while others are completely unspecified in time this class of models is very rich includ ing the fully functional model and the semiparametric model as special cases to estimate the parameters we propose semiparametric profile estimating equations which are solved via an iterative algorithm starting at a consistent estimate from a fully functional model in the existing work no smoothing is needed in contrast to other varying coefficient meth ods the weak convergence of the resultant estimators are developed using the empirical process theory successive tests of time varying effects and backward model selection procedure can then be carried out the practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients

prediction using partly conditional time varying coefficients regression models summary data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts in this paper we propose a method for estimating predictive functions the method uses an extension of the marginal regression analysis methods of liang and zeger 1986 biometrika73 13 22 and is implemented using simple estimating equations a key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions we suggest methods for evaluating the diagnostic accuracy sensitivity and specificity of such rules using cross validation the method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient s current and past clinical status

profile kernel versus backfitting in the partially linear models for longitudinal clustered data summary we study the profile kernel and backfitting methods in partially linear models for clustered longitudinal data for independent data despite the potential root n inconsist ency of the backfitting estimator noted by rice 1986 the two estimators have the same asymptotic variance matrix as shown by opsomer ruppert 1999 in this paper theoretical comparisons of the two estimators for multivariate responses are investigated we show that for correlated data backfitting often produces a larger asymptotic variance than the profile kernel method that is for clustered data in addition to its bias problem the backfitting estimator does not have the same asymptotic efficiency as the profile kernel estimator consequently the common practice of using the backfitting method to compute profile kernel estimates is no longer advised we illustrate this in detail by following zeger diggle 1994 and lin carroll 2001 with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for para metric estimation numerical performance of the two estimators is investigated through a simulation study their application to an ophthalmology dataset is also described

the modified sutherland einstein relation for diffusive non equilibria there remains a useful relation between diffusion and mobility for a langevin particle in a periodic medium subject to non conservative forces the usual fluctuation dissipation relation can be easily modified and the mobility matrix is no longer proportional to the diffusion matrix with a correction term depending explicitly on the non equilibrium forces we discuss this correction by considering various simple examples and we visualize the various dependencies on the applied forcing and on the time by means of simulations for example in all cases the diffusion depends on the external forcing more strongly than does the mobility we also give an explicit decomposition of the symmetrized mobility matrix as the difference between two positive matrices one involving the diffusion matrix and the other involving force force correlations

a frailty model for informative censoring to account for the correlation between failure and censoring we propose a new frailty model for clustered data in this model the risk to be censored is affected by the risk of failure this model allows flexibility in the direction and degree of dependence between failure and censoring it includes the traditional frailty model as a special case it allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative it can also analyze data for competing risks to fit the model the em algorithm is used with markov chain monte carlo simulations in the e steps simulation studies and analysis of data for kidney disease patients are provided consequences of incorrectly assuming noninformative censoring are investigated

efficient semiparametric marginal estimation for longitudinal clustered data we consider marginal generalized semiparametric partially linear models for clustered data lin and carroll derived the semiparametric efficient score function for this problem in the multivariate gaussian case but they were unable to construct a semiparametric efficient estimator that actually achieved the semiparametric information bound here we propose such an estimator and generalize the work to marginal generalized partially linear models we investigate asymptotic relative efficiencies of the estimators that ignore the within cluster correlation structure either in nonparametric curve estimation or throughout we evaluate the finite sample performance of these estimators through simulations and illustrate it using a longitudinal cd4 cell count dataset both theoretical and numerical results indicate that properly taking into account the within subject correlation among the responses can substantially improve efficiency

quaternionic time harmonic maxwell operator the theory of quaternionic alpha hyperholomorphic functions synonyms monogenic regular spatial holomorphic vectors is currently developing rapidly in particular many integral formulae with explicit reproducing kernels have been obtained in this work we establish a one to one correspondence between time harmonic monochromatic electromagnetic fields and pairs of mutually conjugate hyperholomorphic functions this leads to the cauchy type integral associated with maxwell s equations some main integral formulae for maxwell s equations involving this cauchy type integral are obtained it should be mentioned that in fact we introduce and study a somewhat more general quaternionic object which has better algebraic and analytic properties than the physical maxwell operator and which contains the latter as a special case

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

on the hilbert formulas on the unit sphere for the time harmonic relativistic dirac bispinors theory abstract in this paper there are established some analogues of the hilbert formulas on the unit sphere for the theory of time harmonic monochromatic relativistic dirac bispinors the formulas relate a pair of the components of the limit value of a time harmonic dirac bispinor in the unit ball to the other pair of components the obtained results are based on the intimate connection between time harmonic solutions of the relativistic dirac equation and the three dimensional hyperholomorphic function theory hilbert formulas for hyperholomorphic function theory for being a complex quaternionic number are also presented such formulas relate a pair of components of the boundary value of an hyperholomorphic function in the unit ball to the other pair of components in an analogy with what is known for the case of the theory of functions of one complex variable

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

families of multivariate distributions abstract for many years there has been an interest in families of bivariate distributions with marginals as parameters genest and mackay 1986a b showed that several such families that appear in the literature can be derived by a unified method a similar conclusion is obtained in this article through the use of mixture models these models might be regarded as multivariate proportional hazards models with random constants of proportionality the mixture models are useful for two purposes first they make some properties of the derived distributions more transparent the positive dependency property of association is sometimes exposed and a method for simulation of data from the distributions is suggested but the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters and they indicate obvious multivariate extensions some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter

finite dimensional approximation of the self diffusion coefficient for the exclusion process we show that for the symmetric simple exclusion process on z d the self diffusion coefficient of a tagged particle is stable when approximated by simple exclusion processes on large periodic lattices the proof depends on a similar stability property of the asymptotic variance of additive functionals of mean 0 this requires establishing a property for the dirichlet space known as the liouville d property

scalable information inequalities for uncertainty quantification abstract in this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models scalability of inequalities allows us to a obtain uncertainty quantification bounds for quantities of interest in the large degree of freedom limit and or at long time regimes b assess the impact of large model perturbations as in nonlinear response regimes in statistical mechanics c address model form uncertainty i e compare different extended models and corresponding quantities of interest we demonstrate some of these properties by deriving robust uncertainty quantification bounds for phase diagrams in statistical mechanics models

a limit theorem for the position of a tagged particle in a simple exclusion process on montre l extremalite d une mesure invariante pour le processus n a partir d une particule etiquetee et on utilise les proprietes d ergodicite du processus initial pour montrer que la position suit une loi des grands nombres

driven tracer particle in one dimensional symmetric simple exclusion consider an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard core interaction we investigate the behavior of a tagged particle under the action of an external constant driving force we prove that the diffusively rescaled position of the test particle ex e 2t t 0 converges in probability as e 0 to a deterministic function v t the function v depends on the initial distribution of the random environment through a non linear parabolic equation this law of large numbers for the position of the tracer particle is deduced from the hydrodynamical limit of an inhomogeneous one dimensional symmetric zero range process with an asymmetry at the origin an einstein relation is satisfied asymptotically when the external force is small

einstein relation for random walk in a one dimensional percolation model we consider random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph in a companion paper we have shown that if the random walk is pulled to the right by a positive bias uplambda 0 then its asymptotic linear speed overline mathrm v is continuous in the variable uplambda 0 and differentiable for all sufficiently small uplambda 0 in the paper at hand we complement this result by proving that overline mathrm v is differentiable at uplambda 0 further we show the einstein relation for the model i e that the derivative of the speed at uplambda 0 equals the diffusivity of the unbiased walk

a nonparametric dynamic additive regression model for longitudinal data in this work we study additive dynamic regression models for longitudinal data these models provide a flexible and nonparametric method for investigating the time dynamics of longitudinal data the methodology is aimed at data where measurements are recorded at random time points we model the conditional mean of responses given the full internal history and possibly time varying covariates we derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulative time varying regression functions based on the asymptotic results confidence bands may be computed and inference about time varying coefficients may be drawn we propose two estimators of the cumulative regression function one estimator that involves smoothing and one that does not the latter however has twice the variance as the smoothing based estimator goodness of fit of the model is considered using martingale residuals finally we also discuss how partly conditional mean models in which the mean of the response is regressed onto selected time varying covariates may be analysed in the same framework we apply the methods to longitudinal data on height development for cystic fibrosis patients

einstein relation and steady states for the random conductance model we consider random walk among i i d uniformly elliptic conductances on zdzd and prove the einstein relation see theorem 1 it says that the derivative of the velocity of a biased walk as a function of the bias equals the diffusivity in equilibrium for fixed bias we show that there is an invariant measure for the environment seen from the particle these invariant measures are often called steady states the einstein relation follows at least for d 3d 3 from an expansion of the steady states as a function of the bias see theorem 2 which can be considered our main result this expansion is proved for d 3d 3 in contrast to guo ann probab 44 2016 324 359 we need not only convergence of the steady states but an estimate on the rate of convergence see theorem 4

efficient semiparametric mean association estimation for longitudinal binary responses semiparametric methods for longitudinal data with association within subjects have recently received considerable attention however existing methods for semiparametric longitudinal binary regression modeling i mainly concern mean structures with association parameters treated as nuisance ii generally require a correct specification of the covariance structure for misspecified covariance structure may lead to inefficient mean parameter estimates and iii usually run into computation and estimation problems when the time points are irregularly and possibly subject specific in this article we propose a semiparametric logistic regression model which simultaneously takes into account both the mean and response association structures via conditional log odds ratio for multivariate longitudinal binary outcomes our main interest lies in efficient estimation of both the marginal and association parameters the estimators of the parameters are obtained via the profile kernel approach we evaluate the proposed methodology through simulation studies and apply it to a real dataset both theoretical and empirical results demonstrate that the proposed method yields highly efficient estimators and performs satisfactorily copyright 2012 john wiley sons ltd

marginal regression analysis of longitudinal data with time dependent covariates a generalized method of moments approach summary we develop a new approach to using estimating equations to estimate marginal regression models for longitudinal data with time dependent covariates our approach classifies time dependent covariates into three types types i ii and iii the type of covariate determines what estimating equations can be used involving the covariate we use the generalized method of moments to make optimal use of the estimating equations that are made available by the covariates previous literature has suggested the use of generalized estimating equations with the independent working correlation when there are time dependent covariates we conduct a simulation study that shows that our approach can provide substantial gains in efficiency over generalized estimating equations with the independent working correlation when a time dependent covariate is of types i or ii and our approach remains consistent and comparable in efficiency with generalized estimating equations with the independent working correlation when a time dependent covariate is of type iii we apply our approach to analyse the relationship between the body mass index and future morbidity among children in the philippines

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

inferences for a semiparametric model with panel data summary in a longitudinal study suppose that for each subject repeated measurements of the response variable and covariates are collected at a set of distinct irregularly spaced time points we consider a semiparametric model which relates the mean of the response variable at each time point proportionally to a function of a time dependent covariate vector to analyse such panel data inference procedures for regression parameters are proposed without involving any nonparametric function estimation for the nuisance mean function a dataset from a recent aids clinical trial is used to illustate the new proposal

semiparametric regression models for repeated measures of mortal cohorts with non monotone missing outcomes and time dependent covariates we propose a semiparametric marginal modeling approach for longitudinal analysis of cohorts with data missing due to death and non response to estimate regression parameters interpreted as conditioned on being alive our proposed method accommodates outcomes and time dependent covariates that are missing not at random with non monotone missingness patterns via inverse probability weighting missing covariates are replaced by consistent estimates derived from a simultaneously solved inverse probability weighted estimating equation thus we utilize data points with the observed outcomes and missing covariates beyond the estimated weights while avoiding numerical methods to integrate over missing covariates the approach is applied to a cohort of elderly female hip fracture patients to estimate the prevalence of walking disability over time as a function of body composition inflammation and age

einstein relation for a tagged particle in simple exclusion processes it is known that the rescaled position of a tagged particle in symmetric simple exclusion processes converges to a diffusion if now the tracer particle is driven by a small force then it picks up a velocity the einstein relation states that in the limit this velocity is proportional to the small force and the constant of proportionality can be computed from the diffusion matrix of the tracer particle with no driving force such a relation is believed to be generally valid in this article we establish its validity for all symmetric simple exclusion processes in dimension and we prove a density property for certain invariant states of the driven system

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures