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

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

assessment of stratum covariate interactions in cox s proportional hazards regression model we assess stratum e g treatment interactions with covariates and with the baseline hazard function in the proportional hazards ph regression model for lifetime data we consider models incorporating stratum interactions both with and without stratification of the risk sets in the likelihood function and describe likelihood ratio statistics for tests of the presence of these interactions we also present step down methods for building reduced models which include stratum specific parameters corresponding to covariates which interact with treatment we apply ph models with such interactions to a clinical trial of des in the treatment of prostate cancer to determine optimal treatment conditional on each patient s covariates

bayes estimation from a markov renewal process a procedure for bayes nonparametric estimation from a markov renewal process is developed it is based on a conjugate class of a priori distributions on the parameter space of semi markov transition distributions the class is characterized by a dirichlet family of distributions for random markov matrices and a beta family of levy processes for random cumulative hazard functions the main result is the derivation of the posterior law from an observation of the markov renewal process over a period of time

a modification of the redistribution to the right algorithm using disease markers summary disease markers are time dependent covariates which describe progression towards development of disease traditional methods in survival analysis do not make use of available data on these markers to recover additional information from censored individuals using a heuristic modification of the redistribution to the right algorithm efron 1967 a new approach for recovering information for censored individuals using disease markers is proposed additionally the statistical properties of the proposed method are examined there are two possible advantages to this modification i bias reduction when censoring is informative and ii an increase in efficiency in the case of truly noninformative censoring

partially linear hazard regression with varying coefficients for multivariate survival data summary the paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data a profile pseudo partial likelihood estimation method is proposed the estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo partial likelihood whereas the varying coefficient functions are considered as nuisance parameters that are profiled out of the likelihood it is shown that the estimators of the parameters are root n consistent and the estimators of the non parametric coefficient func tions achieve optimal convergence rates asymptotic normality is obtained for the estimators of the finite parameters and varying coefficient functions consistent estimators of the asymptotic variances are derived and empirically tested which facilitate inference for the model we prove that the varying coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent simulations are con ducted to demonstrate the performance of the estimators proposed a real data set is analysed to illustrate the methodology proposed

nonparametric inference for a class of semi markov processes with censored observations a class of semi markov models those which have proportional hazards and which are forward going if state can be reached from i then i cannot be reached from j are shown to fit into the multiplicative intensity model of counting processes after suitable random time changes standard large sample results for counting processes following this multiplicative model can therefore be used to make inferences on the above class of semi markov models including the case where observations may be censored large sample results for a fourstate model used in clinical trials are presented

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

optimal statistical decisions about some alternative financial models abstract we study neyman pearson testing and bayesian decision making based on observations of the price dynamics x t t 0 t of a financial asset when the hypothesis is the classical geometric brownian motion with a given constant growth rate and the alternative is a different random diffusion process with a given possibly price dependent growth rate examples of asset price observations are introduced and used throughout the paper to demonstrate the applicability of the theory by a rigorous mathematical approach we obtain exact formulae and bounds for the most common statistical characteristics of testing and decision making such as the power of test type ii error probability the bayes factor and its moments power divergences and the bayes risk or bayes error these bounds can be much more easily evaluated than the exact formulae themselves and consequently they are useful for practical applications an important theoretical conclusion of this paper is that for the class of alternatives considered neither the risk nor the errors converge to zero faster than exponentially in the observation time t we illustrate in concrete decision situations that the actual rate of convergence is well approximated by the bounds given in the paper

point process modelling for directed interaction networks abstract network data often take the form of repeated interactions between senders and receivers tabulated over time a primary question to ask of such data is which traits and behaviors are predictive of interaction to answer this question a model is introduced for treating directed interactions as a multivariate point process a cox multiplicative intensity model using covariates that depend on the history of the process consistency and asymptotic normality are proved for the resulting partial likelihood based estimators under suitable regularity conditions and an efficient fitting procedure is described multicast interactions those involving a single sender but multiple receivers are treated explicitly the resulting inferential framework is then employed to model message sending behavior in a corporate e mail network the analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

confidence intervals in generalized method of moments models we consider the construction of confidence intervals for parameters characterized by moment restrictions in the standard approach to generalized method of moments gmm estimation confidence intervals are based on the normal approximation to the sampling distribution of the parameters there is often considerable disagreement between the nominal and actual coverage rates of these intervals especially in cases with a large degree of overidentification we consider alternative confidence intervals based on empirical likelihood methods which exploit the normal approximation to the lagrange multipliers calculated as a byproduct in empirical likelihood estimation in large samples such confidence intervals are identical to the standard gmm ones but in finite samples their properties can be substantially different in some of the examples we consider the proposed confidence intervals have coverage rates much closer to the nominal coverage rates than the corresponding gmm intervals

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

stratified partial likelihood estimation when multiple durations are generated by a single unit they may be related in a way that is not fully captured by the regressors the omitted unit specific variables might vary over the durations they might also be correlated with the variables in the regression component we propose an estimator that responds to these concerns and develop a specification test for detecting unobserved unit specific effects data from malaysia reveal that concentration of child mortality in some families is imperfectly explained by observed explanatory variables and that failure to control for unobserved heterogeneity seriously biases the parameter estimates

flood frequency analysis using the cox regression model procedures for incorporating time varying exogenous information into flood frequency analyses are developed using the cox regression model for counting processes in this statistical model the probability of occurrence of a flood peak in a short interval t t dt depends in an explicit manner on the values at t of k covariate processes z1 zk specifically letting dn t be 1 if a flood peak occurs in t t dt and 0 otherwise dn t a t exp j 1kbjzj t dm t where a the baseline intensity is an unknown function b is a vector of unknown regression parameters and the error dm t is conditionally orthogonal to the past history two applications assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time varying flood frequency estimates are considered

reweighting estimators for cox regression with missing covariates missingness in covariates is a common problem in survival data in this article we propose a reweighting method for estimating the regression parameters in the cox model with missing covariates we also consider the augmented reweighting method by subtracting the projection term onto the nuisance tangent space the proposed method provides consistent and asymptotically normally distributed estimators when the missing data mechanism depends on the outcome variables as well as on the observed covariates with either monotone or arbitrary nonmonotone missingness patterns simulation results indicate that in most situations the proposed reweighting estimators are more efficient than the inverse probability weighting estimators for the regression coefficients of the missing covariates and are as efficient as or more efficient than the inverse probability weighting estimators for the regression coefficients of the completely observed covariates the simple reweighting estimators can be easily implemented in st

nonparametric bayes estimators based on beta processes in models for life history data the article studies the problem of finding bayes estimators for cumulative hazard rates and related quantities w r t prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments a particular class of prior processes termed beta processes is introduced and is shown to constitute a conjugate class an important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated for example time inhomogeneous markov chains we find posterior distributions and derive bayes estimators in such models and present a semiparametric bayesian analysis of the cox regression model

the l 1 method for robust nonparametric regression abstract consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy tailed error distribution the two standard approaches to such a problem are each flawed robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods which are not resistant against outliers existing algorithms for robustifying nonparametric regression procedures use either nonlinear optimization of an influence function or iterative solution of local polynomial fitting using reweighted least squares neither of these two approaches combines computational ease with asymptotic theoretical results furthermore application of the robust procedure has been limited almost exclusively to the case of a single explanatory variable with the response variable in this article a new hybrid method is propose

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

bootstrap critical values for tests based on generalized method of moments estimators monte carlo experiments have shown that tests based on generalized method ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used this paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions particular attention is given to the case of dependent data it is shown that with such data the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data the results of monte carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first order asymptotic theory are used the bootstrap also provides an indication of the accuracy of critical values obtained from first order asymptotic theory

time operators and shift representation of dynamical systems abstract we introduce and characterise time operators for unilateral shifts and exact endomorphisms the associated shift representation of evolution is related to the spectral representation by a generalized fourier transform we illustrate the results for a simple exact system namely the renyi map

a maximum entropy approach to recovering information from multinomial response data abstract the classical maximum entropy me approach to estimating the unknown parameters of a multinomial discrete choice problem which is equivalent to the maximum likelihood multinomial logit ml estimator is generalized the generalized maximum entropy gme model includes noise terms in the multinomial information constraints each noise term is modeled as the mean of a finite set of a priori known points in the interval 1 1 with unknown probabilities where no parametric assumptions about the error distribution are made a gme model for the multinomial probabilities and for the distributions associated with the noise terms is derived by maximizing the joint entropy of multinomial and noise distributions under the assumption of independence the gme formulation reduces to the me in the limit as the sample grows large or when no noise is included in the entropy maximization further even though the gme and the logit estimators are conceptually different the dual gme model is related to a gener

goodness of fit tests in models for life history data based on cumulative hazard rates to check the validity of an assumed parametric model for survival data one may compare t the nonparametric nelson aalen plot of the cumulative hazard rate with a t the estimated parametric cumulative hazard rate being for example the maximum likelihood estimator convergence in distribution of n t a t and more general processes is studied employing the general framework of counting processes which allows for quite general models for life history data and for quite general censoring schemes the results are applied to the construction of 2 type statistics for goodness of fit cramer von mises and kolmogorov smirnov type tests are presented in the case where the unknown parameter is one dimensional

a semiparametric model for the analysis of recurrent event panel data summary in many longitudinal studies interest focuses on the occurrence rate of some phenomenon for the subjects in the study when the phenomenon is nonterminating and possibly recurring the result is a recurrent event data set examples include epileptic seizures and recurrent cancers when the recurring event is detectable only by an expensive or invasive examination only the number of events occurring between follow up times may be available this article presents a semiparametric model for such data based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function a random subject specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data estimators are determined from quasi likelihood estimating functions because only first and second moment assumptions are required for quasi likelihood the method is more robust than those based on the specification of a full parametric likelihood consistency of the estimators depends only on the assumption of the proportional intensity model the semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators as with semiparametric methods in survival analysis the method provides useful diagnostics for specific parametric models including a quasi score statistic for testing specific baseline intensity functions the techniques are used to analyze cancer recurrences and a pheromone based mating disruption experiment in moths a simulation study confirms that for many practical situations the estimators possess appropriate small sample characteristics

the analysis of multiple endpoints in clinical trials treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall type i error rate one option is to select a single primary endpoint for formal statistical inference but this is not always feasible another approach is to apply bonferroni correction i e multiply each p value by the total number of endpoints its conservatism for correlated endpoints is examined for multivariate normal data a third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics quantitative binary and survival endpoints are all considered within this general framework two examples are presented and the relative merits of the proposed strategies are discussed

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

on lambda and internal time operators abstract an extended construction of transformations leading from conservative to dissipative evolutions is presented and new sets of admissible states are determined then is presented a probabilistic approach to the concept of internal time operator in this probabilistic context it is shown that is the expected value of the new time operator the scaling function of its tail distribution and that the choice of a profile function reduces to at most three possibilities

score tests for homogeneity of regression effect in the proportional hazards model a simple model containing the proportional hazards regression model as a special case is presented the purpose of the model is to provide a framework in which specific alternatives to the proportional hazards assumption may be tested rank invariant score tests for linear quadratic or exponential trends can for instance all be undertaken within this framework in the case of the two sample problem the required calculations are shown to take a particularly simple form special consideration is given to the two sample case in which there is an inversion of the regression effect i e where the hazard functions cross at some given point both of the motivating examples are concerned with this problem computational aspects are relatively straightforward and some discussion on this is provided

aalen additive hazards change point model we study a test comparing the full aalen additive hazards model and the change point model and suggest how to estimate the parameters of the change point model we also study a test for no change point effect both tests are provided with large sample properties and a resampling method is applied to obtain p values the finite sample properties of the proposed inference procedures and estimators are assessed through a simulation study the methods are further applied to a dataset concerning myocardial infarction

intrinsic irreversibility of kolmogorov dynamical systems we give the mathematical details and various extensions of the results stated in previous work of courbage and prigogine intrinsic random systems are deterministic and conservative dynamical systems for which we can associate two dissipative markov processes through a one to one change of representation the first leading to equilibrium for t and the second for t the microscopic formulation of the second principle of thermodynamics permits to lift the degeneracy by the exclusion of all states that do not approach equilibrium for t the set of admitted initial conditions d is then characterized by a non equilibrium entropy functional which is infinite for rejected initial states and takes finite values for admitted initial conditions thus rejected initial states correspond to an infinite amount of information to realize this selection rule we consider general probability measures on phase space that are not necessarily absolutely continuous and we extend the theory of transition to markov processes to such measures owing to the non invariance of d under the time inversion the evolution of these states in the new representation can only be given by one of the two possible markov processes

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

correcting for selective compliance in a re employment bonus experiment we propose a two stage instrumental variable estimator that is consistent if there is selective compliance in the treatment group of a randomized experiment and the outcome variable is a censored duration the estimator assumes full compliance in the control group we use the estimator to re analyze data from the illinois re employment bonus experiment

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

survival analysis with error prone time varying covariates a risk set calibration approach occupational environmental and nutritional epidemiologists are often interested in estimating the prospective effect of time varying exposure variables such as cumulative exposure or cumulative updated average exposure in relation to chronic disease endpoints such as cancer incidence and mortality from exposure validation studies it is apparent that many of the variables of interest are measured with moderate to substantial error although the ordinary regression calibration approach is approximately valid and efficient for measurement error correction of relative risk estimates from the cox model with time independent point exposures when the disease is rare it is not adaptable for use with time varying exposures by re calibrating the measurement error model within each risk set a risk set regression calibration method is proposed for this setting an algorithm for a bias corrected point estimate of the relative risk using an rrc approach is presented followed by the derivation of an estimate of its variance resulting in a sandwich estimator emphasis is on methods applicable to the main study external validation study design which arises in important applications simulation studies under several assumptions about the error model were carried out which demonstrated the validity and efficiency of the method in finite samples the method was applied to a study of diet and cancer from harvard s health professionals follow up study hpfs

the asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time the log rank test derived by mantel 1966 and peto 1972 is a special case of the efficient scores test for the proportional hazards model it is used frequently in the analysis of survival duration in clinical trials where patients entering the study are assigned at random to different treatments and are followed until they either fail or the study is terminated most survival studies are designed so that the log rank test is calculated at the termination of the study however it is not unusual for the investigator to monitor the experiment periodically it would be very useful to know the joint distribution of the test statistic at different points in time in order to adjust for the effect of repeated significance testing although the joint distribution has not been derived previously sequential procedures for the analysis of survival data in clinical trials have been given by several authors including armitage 1975 pp 140 6 jones whitehead 1979 and nagelkerke hart 1980 in this paper we establish the asymptotic joint distribution of the more general efficient scores test for the proportional hazards model calculated at different points in time and indicate how this can be used for repeated significance testing

evolution semigroups and time operators on banach spaces we present new general methods to obtain shift representation of evolution semigroups defined on banach spaces we introduce the notion of time operator associated with a generalized shift on a banach space and give some conditions under which time operators can be defined on an arbitrary banach space we also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on banach spaces satisfying some geometric conditions the last part of the paper contains some examples of explicit constructions of time operators on function spaces

competing risks regression for stratified data for competing risks data the fine gray proportional hazards model for subdistribution has gained popularity for its convenience in directly assessing the effect of covariates on the cumulative incidence function however in many important applications proportional hazards may not be satisfied including multicenter clinical trials where the baseline subdistribution hazards may not be common due to varying patient populations in this article we consider a stratified competing risks regression to allow the baseline hazard to vary across levels of the stratification covariate according to the relative size of the number of strata and strata sizes two stratification regimes are considered using partial likelihood and weighting techniques we obtain consistent estimators of regression parameters the corresponding asymptotic properties and resulting inferences are provided for the two regimes separately data from a breast cancer clinical trial and from a bone marrow transplantation registry illustrate the potential utility of the stratified fine gray model

a general framework for random effects survival analysis in the cox proportional hazards setting summary the use of random effects modeling in statistics has increased greatly in recent years the introduction of such modeling into event time analysis has proceeded more slowly however previously random effects models for survival data have either required assumptions regarding the form of the baseline hazard function or restrictions on the classes of models that can be fit in this paper we develop a method of random effect analysis of survival data the hierarchical cox model that is an extension of cox s original formulation in that the baseline hazard function remains unspecified this method also allows an arbitrary distribution for the random effects we accomplish this using markov chain monte carlo methods in a bayesian setting the method is illustrated with three models for a dataset with times to multiple occurrences of mammory tumors for 48 rats treated with a carcinogen and then randomized to either treatment or control this analysis is more satisfying than standard approaches such as studying the first event for each subject which does not fully use the data or assuming independence which in this case would overestimate the precision

quasi maximum likelihood estimation of volatility with high frequency data this paper investigates the properties of the well known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise by extending the classic asymptotic results of quasi maximum likelihood estimation when trying to estimate the integrated volatility and the variance of noise this parametric approach remains consistent efficient and robust as a quasi estimator under misspecified assumptions moreover it shares the model free feature with nonparametric alternatives for instance realized kernels while being advantageous over them in terms of finite sample performance in light of quadratic representation this estimator behaves like an iterative exponential realized kernel asymptotically comparisons with a variety of implementations of the tukey hanning2 kernel are provided using monte carlo simulations and an empirical study with the euro us dollar future illustrates its application in practice

nested frailty models using maximum penalized likelihood estimation the frailty model is a random effect survival model which allows for unobserved heterogeneity or for statistical dependence between observed survival data the nested frailty model accounts for the hierarchical clustering of the data by including two nested random effects nested frailty models are particularly appropriate when data are clustered at several hierarchical levels naturally or by design in such cases it is important to estimate the parameters of interest as accurately as possible by taking into account the hierarchical structure of the data we present a maximum penalized likelihood estimation mpnle to estimate non parametrically a continuous hazard function in a nested gamma frailty model with right censored and left truncated data the estimators for the regression coefficients and the variance components of the random effects are obtained simultaneously the simulation study demonstrates that this semi parametric approach yields satisfactory results in this complex setting in order to illustrate the mpnle method and the nested frailty model we present two applications one is for modelling the effect of particulate air pollution on mortality in different areas with two levels of geographical regrouping the other application is based on recurrent infection times of patients from different hospitals we illustrate that using a shared frailty model instead of a nested frailty model with two levels of regrouping leads to inaccurate estimates with an overestimation of the variance of the random effects we show that even when the frailty effects are fairly small in magnitude they are important since they alter the results in a systematic pattern

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

the problem of a covariate time qualitative interaction in a survival study we introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards although this kind of alternative is somewhat rare designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures upon which we can call in those few cases where such departures are suspected furthermore the proposed test and an approximate version of the test are seen to suffer only moderate losses in power when compared with their optimal counterparts should the alternative be one of proportional hazards our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail the model we use in this work is a special case of the one introduced by anderson and senthilselvan 1982 applied statistics 31 44 51 we propose overcoming an inferential problem stemming from their model by using the methods of davies 1977 biometrika 64 247 254 1987 biometrika 74 33 43 backed up by resampling techniques we also look at an approach relying directly on resampling techniques the distributional aspects of this approach under the null hypothesis are interesting but practically its behaviour is such that its use cannot be generally recommended outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory

a dual approach to inference for partially identified econometric models abstract this paper considers inference for the set i of parameter values that minimize a criterion function chernozhukov et al 2007 cht develop a general theory of estimation and inference using the level set of a criterion function we establish a dual relationship between the level set estimator and its support function and show that the properly normalized support function provides alternative wald type inference methods these methods can be used to obtain confidence sets for i and points inside it for models with finitely many moment inequalities we show that our wald type statistic is asymptotically equivalent to cht s statistic under regularity conditions

on fitting cox s regression model with time dependent coefficients summary this paper examines goodness of fit testing in the cox regression model with timevarying regression coefficients arjas 1988 approach is used to define test statistics of the kolmogorov smirnov and cramer von mises types their asymptotic limits are shown to be well known functionals of standard brownian motion leading to the construction of formal goodness of fit tests some numerical studies are also included to illustrate the performance of the tests for moderate sample sizes

on intrinsic randomness of dynamical systems we discuss the problem of nonunitary equivalence via positivity preserving similarity transformations between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes dynamical systems admitting such nonunitary equivalence with stochastic markov processes are said to beintrinsically random in a previous work it was found that the so called bernoulli systems discrete time are intrinsically random in this sense this result is extended here by showing that a more general class of dynamical systems the so calledk systems andk flows are intrinsically random the connection of intrinsic randomness with local instability of motion is briefly discussed we also show that markov processes associated through nonunitary equivalence tononisomorphic k flows are necessarily non isomorphic