Moments of randomly stopped U-STATISTICS

• 成果类型: Article
• 署名作者: De La Pena, VH; Lai, TL
• 署名单位: Columbia University; Stanford University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1023481120
• 发表日期: 1997
• 页码: 2055-2081
• 关键词: renewal theory; CONVERGENCE; expansions

摘要

In this paper we provide sharp bounds on the L-p-norms of randomly stopped U-statistics. These bounds consist mainly of decoupling inequalities designed to reduce the level of dependence between the U-statistics and the stopping time involved. we apply our results to obtain Wald's equation for U-statistics, moment convergence theorems and asymptotic expansions for the moments of randomly stopped U-statistics. The proofs are based an decoupling inequalities, symmetrization techniques, the use of subsequences and induction arguments.