On the asymptotic distribution theory of a class of consistent estimators of a distribution satisfying a uniform stochastic ordering constraint
成果类型：
Article
署名作者：
Arcones, MA; Samaniego, FJ
署名单位：
State University of New York (SUNY) System; Binghamton University, SUNY; University of California System; University of California Davis
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
2000
页码：
116-150
关键词：
摘要：
We identify the asymptotic behavior of the estimators proposed by Rojo and Samaniego and Mukejee of a distribution F assumed to be uniformly stochastically smaller than a known baseline distribution G. We show that these estimators are root n-convergent to a limit distribution with mean squared error smaller than or equal to the mean squared error of the empirical survival function. By examining the mean squared error of the limit distribution, we are able to identify the optimal estimator within Mukejee's class under a variety of different assumptions on F and G. Similar theoretical results are developed for the two-sample problem where F and G are both unknown. The asymptotic distribution theory is applied to obtain confidence bands for the survival function If based on published data from an accelerated life testing experiment.