DISTRIBUTION OF THE MAXIMUM OF CONCOMITANTS OF SELECTED ORDER-STATISTICS
成果类型：
Article
署名作者：
NAGARAJA, HN; DAVID, HA
署名单位：
Medical College of Wisconsin
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176325380
发表日期：
1994
页码：
478-494
关键词：
摘要：
For a random sample of size n from an absolutely continuous bivariate population (X,Y), let X(i:n) denote the ith order statistic of the X sample values. The Y-value associated with X(i:n) is denoted by Y([i:n]) and is called the concomitant of the ith order statistic. For 1 less-than-or-equal-to k less-than-or-equal-to n, let V(k,n) = Max(Y([n-k+1: n)],..., Y([n:n])). In this paper, we discuss the finite-sample and the asymptotic distributions of V(k,n). We investigate the limit distribution of V(k,n) as n --> infinity, when k is held fixed and when k = [np], 0 < p < 1. In both cases we obtain simple sufficient conditions and determine the associated norming constants. We apply our results to some interesting situations, including the bivariate normal population and the simple linear regression model.