The LIL for canonical U-statistics of order 2

• 成果类型: Article
• 署名作者: Giné, E; Kwapien, S; Latala, R; Zinn, J
• 署名单位: University of Connecticut; University of Connecticut; 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/1008956343
• 发表日期: 2001
• 页码: 520-557
• 关键词: iterated logarithm; LAW; CONVERGENCE; bounds; tail

摘要

Let X, X-i, i epsilon N, be independent identically distributed random variables and let h(x, y) = h(y, x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, lim sup(n) log n(log n)(-1) \ Sigma1 less than or equal toi . \ \g \ \ (infinity) < infinity) less than or equal to C.