NOTE ON THE TAIL BEHAVIOR OF GENERAL WEIGHTED EMPIRICAL PROCESSES
成果类型：
Note
署名作者：
VANZUIJLEN, MCA
署名单位：
Radboud University Nijmegen
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348143
发表日期：
1991
页码：
1102-1105
关键词：
摘要：
Under minimal conditions precise bounds are obtained for the expectation of the supremum of the weighted empirical process over the interval (0, 1/(n(log n)d-1)), where d is the dimension of the underlying random vectors. The allowed growth of the weight function is optimal in the iid case. The results will have broad applications in the theory of all kinds of nonstandard weighted empirical processes, such as empirical processes based on uniform spacings or U-statistics, where it is often not so easy to show directly (as in the iid case) that the considered suprema converge to 0 in probability.