ON WEAK-CONVERGENCE OF AN ESTIMATOR OF THE SURVIVAL FUNCTION WHEN NEW IS BETTER THAN USED OF A SPECIFIED AGE
成果类型：
Article
署名作者：
CHANG, MN
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.2307/2289728
发表日期：
1991
页码：
173-178
关键词：
摘要：
A survival function S is said to be in the New Better than Used of age t0 (NBU-t0) class if S(x + t0) less-than-or-equal-to S(t0)S(x) for all x greater-than-or-equal-to 0. Reneau and Samaniego proposed an estimator S(n) for S when S is known as a member of the NBU-t0 class. Many properties of S(n) were studied by Reneau and Samaniego. The problems of the weak convergence of W(n) = square-root n (S(n) - S), however, was not solved. In this article, we show that the weak convergence of W(n) does not hold in general and establish sufficient conditions for the weak convergence to hold. Three important cases are as follows: (1) If the underlying survival function S is from the subclass of New Strictly Better than Used of age t0 (e.g., gamma and Weibull distributions), then W(n) converges weakly with the same limiting distribution as that of the empirical process. In this case, confidence bands for S can be easily constructed. (2) If S is from the subclass of New is the Same as Used of age t0 (e.g., exponential distributions), then the weak convergence of W(n) holds, and the finite-dimensional limiting distribution is estimable. W(n) does not converge weakly to a Brownian bridge, however. (3) If S satisfies neither (1) nor (2), then the weak convergence of W(n) fails to hold. Examples for this case are given in the last section.