a convex analytic approach to risk aware markov decision processes in classical markov decision process mdp theory we search for a policy that say minimizes the expected infinite horizon discounted cost expectation is of course a risk neutral measure which does not suffice in many applications particularly in finance we replace the expectation with a general risk functional and call such models risk aware mdp models we consider minimization of such risk functionals in two cases the expected utility framework and conditional value at risk a popular coherent risk measure later we consider risk aware mdps wherein the risk is expressed in the constraints this includes stochastic dominance constraints and the classical chance constrained optimization problems in each case we develop a convex analytic approach to solve such risk aware mdps in most cases we show that the problem can be formulated as an infinite dimensional linear program lp in occupation measures when we augment the state space we provide a discretization method and finite approximati

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

entropy solutions for stochastic porous media equations we provide an entropy formulation for porous medium type equations with a stochastic non linear spatially inhomogeneous forcing well posedness and l1 contraction is obtained in the class of entropy solutions our scope allows for porous medium operators u m 1u for all m 1 and holder continuous diffusion nonlinearity with exponent 1 2

approximation schemes for infinite linear programs this paper presents approximation schemes for an infinite linear program in particular it is shown that under suitable assumptions the program s optimum value can be approximated by the values of finite dimensional linear programs and that in addition every accumulation point of a sequence of optimal solutions for the approximating programs is an optimal solution for the original problem

convergence of controlled models and finite state approximation for discounted continuous time markov decision processes with constraints abstract in this paper we consider the convergence of a sequence m n of the models of discounted continuous time constrained markov decision processes mdp to the limit one denoted by m for the models with denumerable states and unbounded transition rates under reasonably mild conditions we prove that the constrained optimal policies and the optimal values of m n converge to those of m respectively using a technique of occupation measures as an application of the convergence result developed here we show that an optimal policy and the optimal value for countable state continuous time mdp can be approximated by those of finite state continuous time mdp finally we further illustrate such finite state approximation by solving numerically a controlled birth and death system and also give the corresponding error bound of the approximation

efficient estimation of the partly linear additive cox model the partly linear additive cox model is an extension of the linear cox model and allows flexible modeling of covariate effects semiparametrically we study asymptotic properties of the maximum partial likelihood estimator of this model with right censored data using polynomial splines we show that with a range of choices of the smoothing parameter the number of spline basis functions required for estimation of the nonparametric components the estimator of the finite dimensional regression parameter is root n consistent asymptotically normal and achieves the semiparametric information bound rates of convergence for the estimators of the nonparametric components are obtained they are comparable to the rates in nonparametric regression implementation of the estimation approach can be done easily and is illustrated by using a simulated example

l1 contraction and uniqueness for quasilinear elliptic parabolic equations abstract we prove the l 1 contraction principle and uniqueness of solutions for quasilinear elliptic parabolic equations of the form formula where b is monotone nondecreasing and continuous we assume only that u is a weak solution of finite energy in particular we do not suppose that the distributional derivative t b u is a bounded borel measure or a locally integrable function

stochastic nestedness and the belief sharing information pattern solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time horizon thus leading to non tractability of classical dynamic programming a common joint information state supplied to each of the agents leads to a tractable recursion as is evident in the one step delayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure however communication requirements for such conditions require exchange of very large data noiselessly hence these assumptions are generally impractical in this paper we present a weaker notion of nestedness which we term as stochastic nestedness which is characterized by a sequence of markov chain conditions it is shown that if the information structure is stochastically nested then an optimization problem is tractable and in particular for lqg problems the team optimal solution is linear despite the lack of deterministic nestedness or partial nestedness one other contribution of this paper is that by regarding the multiple decision makers as a single decision maker and using witsenhausen s equivalent model for discrete stochastic control it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions a pattern we refer to as k stage belief sharing pattern we discuss the minimum amount of information exchange required to achieve such an information pattern for k 1 the information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies in view of nestedness we present a discussion on the monotone values of information channels

stochastic conservation laws weak in time formulation and strong entropy condition abstract this article is an attempt to complement some recent developments on conservation laws with stochastic forcing in a pioneering development feng and nualart 8 have developed the entropy solution theory for such problems and the presence of stochastic forcing necessitates introduction of strong entropy condition however the authors formulation of entropy inequalities are weak in space but strong in time in the absence of a priori path continuity for the solutions we take a critical outlook towards this formulation and offer an entropy formulation which is weak in time and weak in space

constrained optimization for average cost continuous time markov decision processes to the best of our knowledge this note is a first study on a multiconstrained optimization problem for average cost continuous time markov decision processes in polish spaces the optimality criterion is the long run expected average cost and the constraints are imposed on similar average costs we give suitable conditions under which the existence of a constrained optimal stationary policy is shown by introducing occupation measures and using a martingale technique also we illustrate our conditions with controlled potlach processes

further results on exponential estimates of markovian jump systems with mode dependent time varying delays this technical note studies the problem of exponential estimates for markovian jump systems with mode dependent interval time varying delays a novel lyapunov krasovskii functional lkf is constructed with the idea of delay partitioning and a less conservative exponential estimate criterion is obtained based on the new lkf illustrative examples are provided to show the effectiveness of the proposed results

information bounds for cox regression models with missing data we derive information bounds for the regression parameters in cox models when data are missing at random these calculations are of interest for understanding the behavior of efficient estimation in case cohort designs a type of two phase design often used in cohort studies the derivations make use of key lemmas appearing in robins rotnitzky and zhao j amer statist assoc 89 1994 846 866 and robins hsieh and newey j roy statist soc ser b 57 1995 409 424 but in a form suited for our purposes here we begin by summarizing the results of robins rotnitzky and zhao in a form that leads directly to the projection method which will be of use for our model of interest we then proceed to derive new information bounds for the regression parameters of the cox model with data missing at random mar in the final section we exemplify our calculations with several models of interest in cohort studies including an i i d version of the classical case cohort design of prentice biometrika 73 1986 1 11 and self and prentice ann statist 16 1988 64 81

censored linear regression for case cohort studies summary right censored data from a classical case cohort design and a stratified case cohort design are considered in the classical case cohort design the subcohort is obtained as a simple random sample of the entire cohort whereas in the stratified design this subcohort is elected by independent bernoulli sampling with arbitrary selection probabilities for each design and under a linear regression model methods for estimating the regression parameters are proposed and analysed these methods are derived by modifying the linear ranks tests and estimating equations that arise from full cohort data using methods that are similar to the pseudolikelihood estimating equation that has been used in relative risk regression for these models the estimators so obtained are shown to be consistent and asymptotically normal variance estimation and numerical illustrations are also provided

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

a note on semiparametric efficient inference for two stage outcome dependent sampling with a continuous outcome outcome dependent sampling designs have been shown to be a cost effective way to enhance study efficiency we show that the outcome dependent sampling design with a continuous outcome can be viewed as an extension of the two stage case control designs to the continuous outcome case we further show that the two stage outcome dependent sampling has a natural link with the missing data and biased sampling framework through the use of semiparametric inference and missing data techniques we show that a certain semiparametric maximum likelihood estimator is computationally convenient and achieves the semiparametric efficient information bound we demonstrate this both theoretically and through simulation

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

discrete time controlled markov processes with average cost criterion a survey this work is a survey of the average cost control problem for discrete time markov processes the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades the exposition ranges from finite to borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies the authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography the authors have also identified several important questions that are still open to investigation

multichain markov decision processes with a sample path constraint a decomposition approach we consider finite state finite action markov decision processes which accumulate both a reward and a cost at each decision epoch we study the problem of finding a policy that maximizes the expected long run average reward subject to the constraint that the long run average cost be no greater than a given value with probability one we establish that if there exists a policy that meets the constraint then there exists an e optimal stationary policy furthermore an algorithm is outlined to locate the e optimal stationary policy the proof of the result hinges on a decomposition of the state space into maximal recurrent classes and a set of transient states

dynamic quantization and power allocation for multisensor estimation of hidden markov models this paper investigates an optimal quantizer design problem for multisensor estimation of a hidden markov model hmms whose description depends on unknown parameters the sensor measurements are simply binary quantized and transmitted to a remote fusion center over noisy flat fading wireless channels under an average sum transmit power constraint the objective is to determine a set of optimal quantization thresholds and sensor transmit powers called an optimal policy which minimizes the long run average of a weighted combination of the expected state estimation error and sum transmit power we analyze the problem by formulating an adaptive markov decision process mdp problem in this framework adaptive optimal control policies are obtained using a nonstationary value iteration nvi scheme and are termed as nvi adaptive policies these nvi adaptive policies are adapted to the hmm parameter estimates obtained via a strongly consistent maximum likelihood estimator in particular hmm parameter estimation is performed by a recursive expectation maximization em algorithm which computes estimates of the hmm parameters by maximizing a relative entropy information measure using the received quantized observations and the trajectory of the mdp under some regularity assumptions on the observation probability distributions and a geometric ergodicity condition on an extended markov chain the maximum likelihood estimator is shown to be strongly consistent it is shown that the nvi adaptive policy based on this sequence of strongly consistent hmm parameter estimates is asymptotically under appropriate assumptions average optimal essentially it minimizes the long run average cost of the weighted combination of the expected state estimation error and sum transmit power across the sensors for the hmm with true parameters in a time asymptotic sense the advantage of this scheme is that the policies are obtained recursively without the need to solve the bellman equation at each time step which can be computationally prohibitive as is usual with value iteration schemes practical implementation of the nvi adaptive policy requires discretization of the state and action space which results in some loss of optimality nevertheless numerical results illustrate the asymptotic convergence properties of the parameter estimates and the asymptotically close to optimal performance of the adaptive mdp algorithm compared to the performance of an mdp based dynamic quantization and power allocation algorithm designed with perfect knowledge of the true parameters

constrained undiscounted stochastic dynamic programming in this paper we investigate the computation of optimal policies in constrained discrete stochastic dynamic programming with the average reward as utility function the state space and action sets are assumed to be finite constraints which are linear functions of the state action frequencies are allowed in the general multichain case an optimal policy will be a randomized nonstationary policy an algorithm to compute such an optimal policy is presented furthermore sufficient conditions for optimal policies to be stationary are derived there are many applications for constrained undiscounted stochastic dynamic programming e g in multiple objective markovian decision models

stochastic generalized porous media and fast diffusion equations abstract we present a generalization of krylov rozovskii s result on the existence and uniqueness of solutions to monotone stochastic differential equations as an application the stochastic generalized porous media and fast diffusion equations are studied for finite reference measures where the drift term is given by a negative definite operator acting on a time dependent function which belongs to a large class of functions comparable with the so called n functions in the theory of orlicz spaces

stochastic dominance constrained markov decision processes we are interested in risk constraints for infinite horizon discrete time markov decision processes mdps starting with average reward mdps we show that increasing concave stochastic dominance constraints on the empirical distribution of reward lead to linear constraints on occupation measures an optimal policy for the resulting class of dominance constrained mdps is obtained by solving a linear program we compute the dual of this linear program to obtain average dynamic programming optimality equations that reflect the dominance constraint in particular a new pricing term appears in the optimality equations corresponding to the dominance constraint we show that many types of stochastic orders can be used in place of the increasing concave stochastic order we also carry out a parallel development for discounted reward mdps with stochastic dominance constraints a portfolio optimization example is used to motivate the paper

the lagrange and the vanishing discount techniques to controlled diffusions with cost constraints abstract in this paper we introduce two useful methods to compute optimal control policies for either the discounted or the average payoff criterion with cost constraints when the dynamic system evolves as a n dimensional diffusion processes as for the attribute cost constraints we mean the coexistence of a given cost function that in general is dominated above by another function in particular by a constant playing the role of an extra constraint in the control model to deduce optimality results for the discounted case we employ the lagrange multipliers technique along with dynamic programming arguments then the vanishing discount method is applied to easily obtain average optimal policies we support our theory by providing an example on pollution accumulation problem

constrained discounted dynamic programming this paper deals with constrained optimization of markov decision processes with a countable state space compact action sets continuous transition probabilities and upper semicontinuous reward functions the objective is to maximize the expected total discounted reward for one reward function under several inequality constraints on similar criteria with other reward functions suppose a feasible policy exists for a problem with m constraints we prove two results on the existence and structure of optimal policies first we show that there exists a randomized stationary optimal policy which requires at most m actions more than a nonrandomized stationary one this result is known for several particular cases second we prove that there exists an optimal policy which is i stationary nonrandomized from some step onward ii randomized markov before this step but the total number of actions which are added by randomization is at most m iii the total number of actions that are added by nonstationarity is at most m we also establish pareto optimality of policies from the two classes described above for multi criteria problems we describe an algorithm to compute optimal policies with properties i iii for constrained problems the policies that satisfy properties i iii have the pleasing aesthetic property that the amount of randomization they require over any trajectory is restricted by the number of constraints in contrast a randomized stationary policy may require an infinite number of randomizations over time

minimax control of discrete time stochastic systems this paper gives a unified self contained presentation of minimax control problems for discrete time stochastic systems on borel spaces with possibly unbounded costs the main results include conditions for the existence of minimax strategies for finite horizon problems and infinite horizon discounted and undiscounted average cost criteria the results are specialized to control systems with unknown disturbance distributions also known as games against nature two examples illustrate the theory one of them on the mold level control problem which is a key problem in the steelmaking industry

asymptotic distribution theory for cox type regression models with general relative risk form the theory and application of the cox 1972 failure time regression model has almost without exception assumed an exponential form for the dependence of the hazard function on regression variables other regression forms may be more natural or descriptive in some applications for example a linear relative risk regression model provides a convenient framework for studying epidemiologic risk factor interactions this note uses the counting process formulation of andersen and gill 1982 to develop asymptotic distribution theory for a class of intensity function regression models in which the usual exponential regression form is relaxed to an arbitrary non negative twice differentiable form some stability and regularity conditions beyond those of andersen and gill are required to show the consistency of the observed information matrix which in general need not be positive semidefinite

constrained average cost markov control processes in borel spaces this paper considers constrained markov control processes in borel spaces with unbounded costs the criterion to be minimized is a long run expected average cost and the constraints can be imposed on similar average costs or on average rewards or discounted costs or rewards we give conditions under which the constrained problem cp is solvable and equivalent to an equality constrained ec linear program furthermore we show that there is no duality gap between ec and the dual program ec and that in fact the strong duality condition holds finally we introduce an explicit procedure to solve cp in some cases which is illustrated with a detailed example

nonlinear fokker planck equations driven by gaussian linear multiplicative noise abstract existence of a strong solution in h 1 r d is proved for the stochastic nonlinear fokker planck equation d x div d x d t x d t x d w in 0 t r d x 0 x respectively for a corresponding random differential equation here d 1 w is a wiener process in h 1 r d d c 1 r d r d and is a continuous monotonically increasing function satisfying some appropriate sublinear growth conditions which are compatible with the physical models arising in statistical mechanics the solution exists for x l 1 l and preserves positivity if is locally lipschitz the solution is unique pathwise lipschitz continuous with respect to initial data in h 1 r d stochastic fokker planck equations with nonlinear drift of the form d x div a x d t x d t x d w are also considered for lipschitzian continuous functions a r r d

strong solutions for stochastic partial differential equations of gradient type unique existence of analytically strong solutions to stochastic partial differential equations spde with drift given by the subdifferential of a quasi convex function and with general multiplicative noise is proven the proof applies a genuinely new method of weighted galerkin approximations based on the distance defined by the quasi convex function spatial regularization of the initial condition analogous to the deterministic case is obtained the results yield a unified framework which is applied to stochastic generalized porous media equations stochastic generalized reaction diffusion equations and stochastic generalized degenerated p laplace equations in particular higher regularity for solutions of such spde is obtained

stochastic scalar conservation laws we introduce a notion of stochastic entropic solution a la kruzkov but with ito s calculus replacing deterministic calculus this results in a rich family of stochastic inequalities defining what we mean by a solution a uniqueness theory is then developed following a stochastic generalization of l1 contraction estimate an existence theory is also developed by adapting compensated compactness arguments to stochastic setting we use approximating models of vanishing viscosity solution type for the construction while the uniqueness result applies to any spatial dimensions the existence result in the absence of special structural assumptions is restricted to one spatial dimension only

limiting discounted cost control of partially observable stochastic systems this paper presents two main results on partially observable po stochastic systems in the first one we consider a general po system x t 1 f x t a t xi t y t g x t eta t t 0 1 ldots hspace 1in on borel spaces with possibly unbounded cost per stage functions and we give conditions for the existence of alpha discount optimal control policies 0 alpha 1 in the second result we specialize to additive noise systems x t 1 f n x t a t xi t y t g n x t eta t t 0 1 ldots in euclidean spaces with fn x a and gn x converging pointwise to mbox functions f infty x a and g infty x respectively and we give conditions for the limiting po model x t 1 f infty x t a t xi t y t g infty x t eta t to have an alpha discount optimal policy

ergodic control of markov chains with constraints the general case the problem of controlling a markov chain on a countable state space with ergodic or long run average cost is studied in the presence of additional constraints requiring finitely many say m other ergodic costs to satisfy prescribed bounds under extremely general conditions it is proved that an optimal stationary randomized strategy can be found that requires at most m randomizations this generalizes a result of ross

fisher s information in terms of the hazard rate if g t is a regular family of probability densities on the real line with corresponding hazard rates h t then the fisher information for can be expressed in terms of the hazard rate as follows f g 2 g h h 2 g r where the dot denotes this identity shows that the hazard rate transform of a probability density has an unexpected length preserving property we explore this property is continuous and discrete settings some geometric consequences and curvature formulas its connection with martingale theory and its relation to statistical issues in the theory of life time distributions and censored data

a comparison of multiple imputation and fully augmented weighted estimators for cox regression with missing covariates several approaches exist for handling missing covariates in the cox proportional hazards model the multiple imputation mi is relatively easy to implement with various software available and results in consistent estimates if the imputation model is correct on the other hand the fully augmented weighted estimators fawes recover a substantial proportion of the efficiency and have the doubly robust property in this paper we compare the fawes and the mi through a comprehensive simulation study for the mi we consider the multiple imputation by chained equation and focus on two imputation methods bayesian linear regression imputation and predictive mean matching simulation results show that the imputation methods can be rather sensitive to model misspecification and may have large bias when the censoring time depends on the missing covariates in contrast the fawes allow the censoring time to depend on the missing covariates and are remarkably robust as long as getting either the conditional expectations or the selection probability correct due to the doubly robust property the comparison suggests that the fawes show the potential for being a competitive and attractive tool for tackling the analysis of survival data with missing covariates

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

degenerate parabolic stochastic partial differential equations quasilinear case we study the cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical wiener process in particular we adapt the notion of kinetic formulation and kinetic solution and develop a well posedness theory that includes also an l 1 contraction property in comparison to the first order case debussche and vovelle 2010 and to the semilinear degenerate parabolic case hofmanova 2013 the present result contains two new ingredients a generalized ito formula that permits a rigorous derivation of the kinetic formulation even in the case of weak solutions of certain nondegenerate approximations and a direct proof of strong convergence of these approximations to the desired kinetic solution of the degenerate problem

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

estimation in the semiparametric accelerated failure time model with missing covariates improving efficiency through augmentation abstractthis article considers linear regression with missing covariates and a right censored outcome we first consider a general two phase outcome sampling design where full covariate information is only ascertained for subjects in phase two and sampling occurs under an independent bernoulli sampling scheme with known subject specific sampling probabilities that depend on phase one information e g survival time failure status and covariates the semiparametric information bound is derived for estimating the regression parameter in this setting we also introduce a more practical class of augmented estimators that is shown to improve asymptotic efficiency over simple but inefficient inverse probability of sampling weighted estimators estimation for known sampling weights and extensions to the case of estimated sampling weights are both considered the allowance for estimated sampling weights permits covariates to be missing at random according to a monotone but unknown mechanism the asymptotic pr

information bounds for the conditional hazard ratio in a nested family of regression models information bounds are obtained for a parametric treatment effect in a nested family of models for the conditional distribution of survival given confounding variables the family extends from the fully parametric weibull model to a completely nonparametric model for right censored data and includes the cox model and the stratified version of it it is shown that in certain special cases there is no loss of information about the treatment effect when going from a fully parametric to a nonparametric specification of the conditional hazard function

case cohort and case control analysis with cox s model prentice 1986 proposed the case cohort design and studied a pseudolikelihood estimator of regression parameters in cox s model we derive a class of estimating equations for case cohort sampling each depending on a different estimator of the population distribution which lead naturally to simple estimators that improve on prentice s pseudolikelihood estimator we also discuss an equivalence between case control and case cohort sampling in terms of the estimation of regression parameters in cox s model

entropy solutions for nonlinear degenerate problems we consider a class of elliptic hyperbolic degenerate equations g u delta b u divg phi u f with dirichlet homogeneous boundary conditions and a class of elliptic parabolic hyperbolic degenerate equations g u t delta b u divg phi u f with homogeneous dirichlet conditions and initial conditions existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function satisfying rather general conditions comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for continuous

finite state approximations to discounted and average cost constrained markov decision processes in this paper we consider the finite state approximation of a discrete time constrained markov decision process mdp under the discounted and average cost criteria using the linear programming formulation of the constrained discounted cost problem we prove the asymptotic convergence of the optimal value of the finite state model to the optimal value of the original model with further continuity condition on the transition probability we also establish a method to compute approximately optimal policies for the average cost instead of using the finite state linear programming approximation method we use the original problem definition to establish the finite state asymptotic approximation of the constrained problem and compute approximately optimal policies under lipschitz type regularity conditions on the components of the mdp we also obtain explicit rate of convergence bounds quantifying how the approximation improves as the size of the approximating finite state space increases

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

the existence of minimum pair of state and policy for markov decision processes under the hypothesis of doeblin this paper studies the average cost markov decision process with compact state and action spaces and bounded lower semicontinuous cost functions following the idea of borkar s excellent papers siamj control optim 21 1983 pp 652 666 22 1984 pp 965 978 the general case where irreducibility is not assumed is considered under the hypothesis of doeblin and the existence of a minimum pair of state and policy which attains the infimum of the average expected cost over all initial states and policies is established further it is proved that under additional weak conditions there exists an optimal stationary policy in the usual sense

scalar conservation laws with stochastic forcing we show that the cauchy problem for a randomly forced periodic multi dimensional scalar first order conservation law with additive or multiplicative noise is well posed it admits a unique solution characterized by a kinetic formulation of the problem which is the limit of the solution of the stochastic parabolic approximation

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

on stochastic conservation laws and malliavin calculus abstract for stochastic conservation laws driven by a semilinear noise term we propose a generalization of the kru kov entropy condition by allowing the kru kov constants to be malliavin differentiable random variables existence and uniqueness results are provided our approach sheds some new light on the stochastic entropy conditions put forth by feng and nualart 17 and bauzet vallet and wittbold 2 and in our view simplifies some of the proofs

infinite linear programming and multichain markov control processes in uncountable spaces in this paper we use infinite linear programming to study markov control processes in borel spaces and the average cost criterion in the unichain and multichain cases under appropriate assumptions we show that in both cases the associated linear programs are solvable and that there is no duality gap moreover conditions are given for minimizing respectively maximizing sequences for the primal respectively dual programs to converge to optimal solutions

retrospective likelihood based methods for analyzing case cohort genetic association studies summary the case cohort cch design is a cost effective design for assessing genetic susceptibility with time to event data especially when the event rate is low in this work we propose a powerful pseudo score test for assessing the association between a single nucleotide polymorphism snp and the event time under the cch design the pseudo score is derived from a pseudo likelihood which is an estimated retrospective likelihood that treats the snp genotype as the dependent variable and time to event outcome and other covariates as independent variables it exploits the fact that the genetic variable is often distributed independent of covariates or only related to a low dimensional subset estimates of hazard ratio parameters for association can be obtained by maximizing the pseudo likelihood a unique advantage of our method is that it allows the censoring distribution to depend on covariates that are only measured for the cch sample while not requiring the knowledge of follow up or covariate information on subjects not selected into the cch sample in addition to these flexibilities the proposed method has high relative efficiency compared with commonly used alternative approaches we study large sample properties of this method and assess its finite sample performance using both simulated and real data examples