WEAK-CONVERGENCE AND GLIVENKO-CANTELLI RESULTS FOR WEIGHTED EMPIRICAL U-PROCESSES
成果类型：
Article
署名作者：
SCHNEEMEIER, W
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989287
发表日期：
1993
页码：
1170-1184
关键词：
摘要：
Empirical processes of U-statistic structure were introduced by Serfling and studied in detail by Silverman, who proved weak convergence of weighted versions in the i.i.d. case. Our main theorem shows that this result can be generalized in two directions: First, the i.i.d. assumption can be omitted, and second, our proof holds for a richer class of weight functions. In addition, we obtain almost sure convergence of weighted U-processes in the i.i.d. case which improves the results of Helmers, Janssen and Serfling, Aerts, Janssen and Mason and (in the special situation of the real line) Nolan and Pollard.