Necessary and sufficient conditions for the strong law of large numbers for U-statistics

• 成果类型: Article
• 署名作者: Latala, R; Zinn, J
• 署名单位: University of Warsaw; Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1019160513
• 发表日期: 2000
• 页码: 1908-1924
• 关键词: quadratic-forms; PRODUCTS; sums

摘要

Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the strong law of large numbers for (symmetrized) U-statistics. We also obtain necessary and sufficient conditions for the a.s. convergence of series of an analogous form.