A REMARK ON CONVERGENCE IN DISTRIBUTION OF U-STATISTICS

• 成果类型: Article
• 署名作者: GINE, E; ZINN, J
• 署名单位: 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/1176988850
• 发表日期: 1994
• 页码: 117-125
• 关键词: symmetric statistics

摘要

It is proved that, for h measurable and symmetric in its arguments and X(i) i.i.d., if the sequence (n(-m/2)SIGMA(i1,...,im less-than-or-equal-to n, ij not-equal ik if j not-equal k) h(X(i1),...,X(im))}n=1infinity is stochastically bounded, then Eh2 < infinity and Eh(X1,x2,...,x(m)) = 0 a.s..