ASYMPTOTIC DISTRIBUTIONS FOR WEIGHTED U-STATISTICS
成果类型：
Article
署名作者：
MAJOR, P
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176988610
发表日期：
1994
页码：
1514-1535
关键词：
摘要：
We prove limit theorems for weighted U-statistics and express the limit by means of multiple stochastic integrals. This is a generalization of the paper by O'Neil and Redner. In that paper the method of moments was applied which does not work in the general case. Hence we had to work out a different method. In particular, in Theorem 4 we describe the limit of a model proposed by O'Neil and Redner. In this model the weight functions cause an intricate cancellation, and the limit can be presented as a sum of multiple stochastic integrals with different multiplicities.
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