V. Susarla SUNY-Binghamton and John Van Ryzin Columbia University This paper extends empirical Bayes estimators with squared error loss and tests with linear loss for two classes of exponential families when the observed data is randomly right censored Sufficient conditions for proving asymptotic optimality of the procedures are given. Various extensions to multiple action problems and to rate of convergence results are indicated.

In several longitudinal studies the median and mean survival times are considered important summary statistics describing the survival experience of the sample under observation. The mean survival time is a commonly used statistic in the case of no censoring. This is due to its ease of computation and the considerable literature available on its properties. However, its competitor, the median survival time may be preferred with censored survival data because it is less sensitive to large observations and to the censoring pattern. The purpose of this article is to introduce an estimator of the median survival time which has applications in a variety of situations encountered in

On considere une classe d'estimateurs non parametriques du type histogramme et on cherche a obtenir des mesures globales

The methodology used to construct tree structured rules is the focus of this monograph. Unlike many other statistical procedures, which moved from pencil and paper to calculators, this text's use of trees was unthinkable before computers. Both the practical and theoretical sides have been developed in the authors' study of tree methods. Classification and Regression Trees reflects these two sides, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.

This paper introduces a multi-step procedure for estimating the regression coefficients in a linear model when the dependent variable of interest is a randomly right censored transform of survival, i.e., log lifetime. The procedure is closely related to that introduced by Buckley and James (1979). Using large sample properties developed by the authors (1981a), asymptotic large sample consistency and normality are seen to hold for each iterate of the original estimator. A limited simulation study examines the small sample behavior of the procedure.

This paper discusses shrinkage estimation in nonparametric Bayesian survival analysis using censored data. The shrinkage estimators proposed are based on estimating the parameter measure of a prior Dirichlet process in a nonparametric Bayesian survival curve estimator which is the posterior mean of this process. The shrinkage is toward a prior family of exponential survival curves. The estimators are then compared by simulation with the wholly nonparametric estimator of Kaplan-Meier and the maximum likelihood estimator for the exponential family. These comparisons are done in cases where the exponential assumption is both

In the Empirical Bayes (EB) approach to estimating the mean of a Poission distribution, smoothing procedures are required to improve the performance of an EB estimator in small samples. Various smooth EB estimators in the literature strongly deopend on the nondecreasing property of the Bayes estimator when a priori gamma density is assumed. Such EB estimators provide good small sample properties but fail to have for general priors the asymptotic optimality property as defined by Robbins (1964). In this paper various smoothed estimators of a discrete density are introduced and applied to this EB problem. The resulting EB estimators are asymptotically optimal. Based on simulation with a gamma prior, they perform rather poorly as compared to other smooth EB rules in small samples and thus in not practical in the small sample environment. However, they are uniformly better than Robbins' estimator and better than the classical MVU estimator in most cases, while retaining the property of asymptotic optimality which those based on a gamma prior do not have.

In the context of lifetesting, an asymptotically risk-efficient procedure for the estimation of the exponential mean lifetime is considered when the survival times of the units are subject to random censorship. The loss function is the sum of squared error due to estimation, cost of recruitment of the units, and cost of total time on test. Asymptotic properties of the sequential estimator and stopping time are described as the per unit cost of total time on test decreases to zero. 1. Introduction. In several statistical experiments pertaining to reliability, life tests, and other longitudinal investigations a sample of units on test are under continual surveillance until one or the other specified terminal response is recorded for each unit. Such experiments may entail a considerable expenditure in costs and time particularly if the per unit cost of recruitment of subjects into the study and of follow-up time are high. It is then desirable to curtail observation at an intermediate state, prior to the last response being recorded, and base analyses on the current accumulated statistical evidence should it seem warranted for the study under consideration. In this article we address the problem of estimation of the mean exponential lifetime 0 from a sample of subjects whose survival times are deterred from complete observation due to random withdrawals or censorship. For each unit, the censoring variable Y is assumed independent of the survival time X, but is otherwise unknown, and the investigator only observes the datum (Z, 8) where Z = min(X, Y) and 8 = 1 or O according as Z = X or Y. Let Z(1)*..., Z(n) denote