The LIL for canonical U-statistics

• 成果类型: Article
• 署名作者: Adamczak, Radoslaw; Latala, Rafal
• 署名单位: Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP351
• 发表日期: 2008
• 页码: 1023-1058
• 关键词: moment inequalities; tail; LAW

摘要

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical U-statistics of arbitrary order d, extending the previously known results for d = 2. The nasc's are expressed as growth conditions on a parameterized family of norms associated with the U-statistics kernel.