estimating relative potency using prior information this paper exhibits a closed form point and interval estimator of the log relative potency that incorporates prior information on the log relative potency in a symmetric parallel line bioassay the point estimator turns out to be a weighted average of the usual estimator and the prior mean where the weights are determined by the prior variance

bayesian random threshold estimation in a cox proportional hazards cure model in this paper we develop a bayesian approach to estimate a cox proportional hazards model that allows a threshold in the regression coefficient based on a threshold in a covariate when some fraction of subjects are not susceptible to the event of interest a data augmentation scheme with latent binary cure indicators is adopted to simplify the markov chain monte carlo implementation given the binary cure indicators the cox cure model reduces to a standard cox model and a logistic regression model furthermore the threshold detection problem reverts to a threshold problem in a regular cox model the baseline cumulative hazard for the cox model is formulated non parametrically using counting processes with a gamma process prior simulation studies demonstrate that the method provides accurate point and interval estimates application to a data set of oropharynx cancer patients suggests a significant threshold in age at diagnosis such that the effect of gender on disease specific survival changes after the threshold

stable trace formula cuspidal tempered terms consider a connected reductive group g over a number field f for technical reasons we assume that the derived group of g is simply connected see l1 in l3 langlands partially stabilizes the trace formula for g after making certain assumptions he writes the elliptic regular part of the trace formula for g as a linear combination of the elliptic g regular parts of the stable trace formulas for the elliptic endoscopic groups h of g the function f used in the stable trace formula forh is obtained from the function f used in the trace formula for g by transferring orbital integrals

a class of semiparametric mixture cure survival models with dependent censoring modern cancer treatments have substantially improved cure rates and have generated a great interest in and need for proper statistical tools to analyze survival data with nonnegligible cure fractions data with cure fractions often are complicated by dependent censoring and the analysis of this type of data typically involves untestable parametric assumptions on the dependence of the censoring mechanism and the true survival times motivated by the analysis of prostate cancer survival trends we propose a class of semiparametric transformation cure models that allows for dependent censoring without making parametric assumptions on the dependence relationship the proposed class of models encompasses a number of common models for the latency survival function including the proportional hazards model and the proportional odds model and also allows for time dependent covariates an inverse censoring probability reweighting scheme is used to derive unbiased estimating equations small sample properties wit

inverse regression estimation for censored data an inverse regression methodology for assessing predictor performance in the censored data setup is developed along with inference procedures and a computational algorithm the technique developed here allows for conditioning on the unobserved failure time along with a weighting mechanism that accounts for the censoring the implementation is nonparametric and computationally fast this provides an efficient methodological tool that can be used especially in cases where the usual modeling assumptions are not applicable to the data under consideration it can also be a good diagnostic tool that can be used in the model selection process we have provided theoretical justification of consistency and asymptotic normality of the methodology simulation studies and two data analyses are provided to illustrate the practical utility of the procedure

estimation in a cox regression model with a change point according to a threshold in a covariate we consider a nonregular cox model for independent and identically distributed right censored survival times with a change point according to the unknown threshold of a covariate the maximum partial likelihood estimators of the parameters and the estimator of the baseline cumulative hazard are studied we prove that the estimator of the change point is n consistent and the estimator of the regression parameters are n 1 2 consistent and we establish the asymptotic distributions of the estimators the estimators of the regression parameters and of the baseline cumulative hazard are adaptive in the sense that they do not depend on the knowledge of the change point

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

testing for threshold effects in regression models in this article we develop a general method for testing threshold effects in regression models using sup likelihood ratio lr type statistics although the sup lr type test statistic has been considered in the literature our method for establishing the asymptotic null distribution is new and nonstandard the standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function the article provides an alternative novel method that can be used to establish the asymptotic null distribution even when the usual quadratic approximation is intractable we illustrate the usefulness of our approach in the examples of the maximum score estimation maximum likelihood estimation quantile regression and maximum rank correlation estimation we establish consistency and local power properties of the test we provide some simulation results and also an empirical application to tipping in racial segregation this ar

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

likelihood ratio tests for a changepoint with survival data summary we consider the likelihood ratio test for a changepoint or lag of the effect of some covariates e g treatment in regression modelling of survival data subject to right censoring asymptotic distributions under null hypotheses are derived numerical examples are used to illustrate the implementation of the procedure finally we apply the theory to data from a large randomised cancer prevention trial

inference under right censoring for transformation models with a change point based on a covariate threshold we consider linear transformation models applied to right censored survival data with a change point in the regression coefficient based on a covariate threshold we establish consistency and weak convergence of the nonparametric maximum likelihood estimators the change point parameter is shown to be n consistent while the remaining parameters are shown to have the expected root n consistency we show that the procedure is adaptive in the sense that the nonthreshold parameters are estimable with the same precision as if the true threshold value were known we also develop monte carlo methods of inference for model parameters and score tests for the existence of a change point a key difficulty here is that some of the model parameters are not identifiable under the null hypothesis of no change point simulation studies establish the validity of the proposed score tests for finite sample sizes

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

change point estimation under adaptive sampling we consider the problem of locating a jump discontinuity change point in a smooth parametric regression model with a bounded covariate it is assumed that one can sample the covariate at different values and measure the corresponding responses budget constraints dictate that a total of n such measurements can be obtained a multistage adaptive procedure is proposed where at each stage an estimate of the change point is obtained and new points are sampled from its appropriately chosen neighborhood it is shown that such procedures accelerate the rate of convergence of the least squares estimate of the change point further the asymptotic distribution of the estimate is derived using empirical processes techniques the latter result provides guidelines on how to choose the tuning parameters of the multistage procedure in practice the improved efficiency of the procedure is demonstrated using real and synthetic data this problem is primarily motivated by applications in engineering systems

adaptive estimation of the threshold point in threshold regression this paper studies semiparametric efficient estimation of the threshold point in threshold regression the classical literature of semiparametric efficient estimation rests on the fact that the maximum likelihood estimator is efficient in any parametric submodel for a large class of loss functions however in threshold regression the maximum likelihood estimator is not efficient while the bayes estimators are efficient and different loss functions induce different efficient estimators for an additively separable loss function that separates the efficiency problem of the threshold point from that of other parameters we show that the semiparametric and parametric efficiency risk bounds coincide then we design a semiparametric empirical bayes estimator to achieve this bound in consequence the threshold point can be adaptively estimated even under conditional moment restrictions we also provide a valid confidence interval called the nonparametric posterior interval for the threshold point simulation studies show that the semiparametric empirical bayes approach is substantially better than existing methods to illustrate our procedure in practice we apply it to an economic growth model for detecting different growth patterns

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

on asymptotically optimal tests under loss of identifiability in semiparametric models we consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models where regularity conditions for profile likelihood theory fail exponential average tests based on integrated profile likelihood are constructed and shown to be asymptotically optimal under a weighted average power criterion with respect to a prior on the nonidentifiable aspect of the model these results extend existing results for parametric models which involve more restrictive assumptions on the form of the alternative than do our results moreover the proposed tests accommodate models with infinite dimensional nuisance parameters which either may not be identifiable or may not be estimable at the usual parametric rate examples include tests of the presence of a change point in the cox model with current status data and tests of regression parameters in odds rate models with right censored data optimal tests have not previously been studied for these scenarios we study the asymptotic distribution of the proposed tests under the null fixed contiguous alternatives and random contiguous alternatives we also propose a weighted bootstrap procedure for computing the critical values of the test statistics the optimal tests perform well in simulation studies where they may exhibit improved power over alternative tests

predicting survival probabilities with semiparametric transformation models abstract prediction of survival probabilities for future patients is one of the main goals of fitting survival data with regression models in this article we consider a large class of semiparametric transformation models which includes the well known proportional hazards and proportional odds models for the analysis of failure time data specifically we propose pointwise and simultaneous confidence interval procedures for the survival probability of future patients with specific covariates these procedures can be easily implemented through simulation and are illustrated with the data from two well known clinical studies

semiparametric estimation of a binary response model with a change point due to a covariate threshold this paper is concerned with semiparametric estimation of a threshold binary response model the estimation method considered in the paper is semiparametric since the parameters for a regression function are finite dimensional while allowing for heteroskedasticity of unknown form in particular the paper considers manski 1975 1985 s maximum score estimator the model in this paper is irregular because of a change point due to an unknown threshold in a covariate this irregularity coupled with the discontinuity of the objective function of the maximum score estimator complicates the analysis of the asymptotic behavior of the estimator sufficient conditions for the identification of parameters are given and the consistency of the estimator is obtained it is shown that the estimator of the threshold parameter is n consistent and the estimator of the remaining regression parameters is cube root n consistent furthermore we obtain the asymptotic distribution of the estimators it turns out that a suitably normalized estimator of the regression parameters converges weakly to the distribution to which it would converge weakly if the true threshold value were known and likewise for the threshold estimator

multi threshold accelerated failure time model a two stage procedure for simultaneously detecting multiple thresholds and achieving model selection in the segmented accelerated failure time aft model is developed in this paper in the first stage we formulate the threshold problem as a group model selection problem so that a concave 2 norm group selection method can be applied in the second stage the thresholds are finalized via a refining method we establish the strong consistency of the threshold estimates and regression coefficient estimates under some mild technical conditions the proposed procedure performs satisfactorily in our simulation studies its real world applicability is demonstrated via analyzing a follicular lymphoma data

robust inference for univariate proportional hazards frailty regression models we consider a class of semiparametric regression models which are one parameter extensions of the cox j roy statist soc ser b 34 1972 187 220 model for right censored univariate failure times these models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty the frailty is assumed to have mean 1 within a known one parameter family of distributions inference is based on a nonparametric likelihood the behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified the joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo value maximizing the asymptotic limit of the likelihood appropriately standardized the estimator converges weakly to a gaussian process when the model is correctly specified the procedure is semiparametric efficient achieving the semiparametric information bound for all parameter components it is also proved that the bootstrap gives valid inferences for all parameters even under misspecification we demonstrate analytically the importance of the robust inference in several examples in a randomized clinical trial a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified under certain conditions on the covariates the ratios of the regression parameters are still identifiable the practical utility of the procedure is illustrated on a non hodgkin s lymphoma dataset

empirical bayes estimation for combinations of multivariate bioassays summary this article presents a new empirical bayes estimator ebe and a shrinkage estimator for determining the relative potency from several multivariate bioassays by incorporating prior information on the model parameters based on jeffreys rules the ebe can account for any extra variability among the bioassays and if this extra variability is 0 then the ebe reduces to the maximum likelihood estimator for combinations of multivariate bioassays the shrinkage estimator turns out to be a compromise of the prior information and the estimator from each multivariate bioassay with the weights depending on the prior variance

proportional hazards model with a change point for clustered event data in many epidemiology studies family data with survival endpoints are collected to investigate the association between risk factors and disease incidence sometimes the risk of the disease may change when a certain risk factor exceeds a certain threshold finding this threshold value could be important for disease risk prediction and diseases prevention in this work we propose a change point proportional hazards model for clustered event data the model incorporates the unknown threshold of a continuous variable as a change point in the regression the marginal pseudo partial likelihood functions are maximized for estimating the regression coefficients and the unknown change point we develop a supremum test based on robust score statistics to test the existence of the change point the inference for the change point is based on the m out of n bootstrap we establish the consistency and asymptotic distributions of the proposed estimators the finite sample performance of the proposed method is demonstrated via extensive simulation studies finally the strong heart family study dataset is analyzed to illustrate the methods

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

on the linear transformation model for censored data recently cheng wei ying 1995 1997 proposed a class of estimation procedures for semi parametric linear transformation models with censored observations when the support of the censoring variable is shorter than that of the failure time the estimators are asymptotically biased in this paper we present a simple modification of cheng s estimation procedures for the regression parameters through extensive numerical studies with practical sample sizes we find that the new proposals perform well but the original interval estimators may not have correct coverage probabilities when censoring is heavy prediction procedures for the survival probabilities of future subjects are also modified accordingly

proportional odds regression and sieve maximum likelihood estimation summary this paper introduces under a censoring mechanism an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method the procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative kullback leibler risk to select the best approximation the procedure adapts to various unknown structures of the baseline function such as spatial structures and smoothness of an unknown degree the proposed procedure is implemented for right censored and so called case 2 interval censored data the estimated regression parameters are shown to be asymptotically normal and efficient the small sample operating characteristics of the proposed procedure are examined via simulations and are illustrated on a dataset from a study of breast cancer patients

change point in stochastic design regression and the bootstrap in this paper we study the consistency of dierent bootstrap procedures for constructing condence intervals cis for the unique jump discontinuity change point in an otherwise smooth regression function in a stochastic design setting this problem exhibits nonstandard asymptotics and we argue that the standard bootstrap procedures in regression fail to provide valid condence intervals for the change point we propose a version of smoothed bootstrap illustrate its remarkable nite sample performance in our simulation study and prove the consistency of the procedure the m out of n bootstrap procedure is also considered and shown to be consistent we also provide sucient conditions for any bootstrap procedure to be consistent in this scenario

on endoscopic transfer of deligne lusztig functions in this paper we prove the fundamental lemma for deligne lusztig functions namely for every deligne lusztig functionon a p adic group g we write down an explicit linear combinationh of deligne lusztig functions on an endoscopic group h such thatandh have matching orbital integrals in particular we prove a conjecture of kottwitz ko4 more precisely we do it under some mild restriction on p

concomitant information in bioassay and semi parametric estimation this paper presents a flexible modern approach to handling concomitant information for estimating the relative potency parameter in quantitative bioassays this is accomplished in a semi parametric framework where the concomitant variable is included non parametrically estimation is then performed using smoothing splines where the point and interval estimators of the relative potency parameter exhibits desirable asymptotic properties

shrinkage estimators of relative potency abstract this article examines the finite and infinite sample properties of the shrinkage estimator motivated by a bayesian argument for the log relative potency proposed in an earlier paper by kim carter and hubert this estimator can be written in closed form and is shown to have finite mean and finite variance in finite samples as a consequence this shrinkage estimator has finite frequentist risk which is an improvement over the usual maximum likelihood estimator for all finite sample sizes furthermore it is shown that this estimator asymptotically behaves the same as the usual maximum likelihood estimator

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

bayesian inference for ratios of coefficients in a linear model a variety of statistical problems e g slope ratio and parallel line bioassay calibration bioequivalence can be viewed as questions of inference on the ratio of two coefflcients in a suitably constructed linear model this paper develops a bayesian approach for the general formulation of the problem using a class of priors which involve the unknown ratio explicitly the posterior distribution of the ratio is obtained analytically and its properties are investigated especially the sensitivity to the choice of the prior examples are given of applications to slope ratio bioassay comparison of the mean effects of two drugs and a bioequivalence problem

asymptotics for change point models under varying degrees of mis specification change point models are widely used by statisticians to model drastic changes in the pattern of observed data least squares maximum likelihood based estimation of change points leads to curious asymptotic phenomena when the change point model is correctly specified such estimates generally converge at a fast rate n and are asymptotically described by minimizers of a jump process under complete mis specification by a smooth curve i e when a change point model is fitted to data described by a smooth curve the rate of convergence slows down to n1 3 and the limit distribution changes to that of the minimizer of a continuous gaussian process in this paper we provide a bridge between these two extreme scenarios by studying the limit behavior of change point estimates under varying degrees of model mis specification by smooth curves which can be viewed as local alternatives we find that the limiting regime depends on how quickly the alternatives approach a change point model we unravel a family of intermediate limits that can transition at least qualitatively to the limits in the two extreme scenarios the theoretical results are illustrated via a set of carefully designed simulations we also demonstrate how inference for the change point parameter can be performed in absence of knowledge of the underlying scenario by resorting to subsampling techniques that involve estimation of the convergence rate

unipotent representations and unipotent classes in sl n to achieve the stabilization of the trace formula for a reductive group 18 there are two related problems that must first be solved one is the matching of the sorbital integrals of smooth functions on a reductive group g over a p adic field of characteristic zero with stable orbital integrals on its endoscopic groups h igusa theory clarifies the nature of this first problem 11 12 13 19 22 23 the second problem is the fundamental lemma which asserts the compatibility of the matching of smooth functions with the hecke algebras on g and h buildings have been used to study this problem 25 the statements of the problems are closely related and the main results of this paper give a method of reducing one problem to the other if the first problem matching smooth functions is solved for sl n then the second problem the fundamental lemma for the hecke algebras follows as a consequence at least for the identity of the algebra the solutions of the two problems are linked by making a detailed study of the unipotent representations and the unipotent classes of sl n representations with iwahori fixed vectors on sl n f are called unipotent in this paper to emphasize the close relationship between unipotent conjugacy classes and these representations not long after this paper was written waldspurger refined reformulated and greatly extended the results of this paper this paper made a modest contribution to this subsequent work of his he eliminated the hypothesis that functions on sl n have matching smooth functions by making clever use of a strengthened version of kazhdan s lemma the opinion of the experts is still divided will the solution of the fundamental lemma for other reductive groups come from the matching of smooth functions or will it come from even stronger versions of kazhdan s lemma this much is clear the fundamental lemma no longer needs to be viewed as an isolated combinatorial problem in buildings howe s conjecture uniform germ expansions homogeneity of germs compact traces unipotent orbits and kazhdan s density theorem give us a framework through which the fundamental lemma may be understood in the final portion of the introduction i would like to state a theorem that has considerable interest beyond its usefulness for the fundamental lemma this theorem will be used in section 1 to produce a uniform germ expansion the

the hodge conjecture and arithmetic quotients of complex balls let s be a closed shimura variety uniformized by the complex n ball associated with a standard unitary group the hodge conjecture predicts that every hodge class in h 2k s mathbb q k 0 dots n is algebraic we show that this holds for all degrees k away from the neighborhood bigl tfrac13n tfrac23n bigr of the middle degree we also prove the tate conjecture for the same degrees as the hodge conjecture and the generalized form of the hodge conjecture in degrees away from an interval depending on the codimension c of the subvariety centered at the middle dimension of s these results are derived from a general theorem that applies to all shimura varieties associated with standard unitary groups of any signature the proofs make use of arthur s endoscopic classification of automorphic representations of classical groups as such our results rely on the stabilization of the trace formula for the disconnected groups gl n rtimes langle theta rangle associated with base change

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field