Weak Convergence of Generalized $U$-Statistics

作者：Pranab Kumar Sen · 发表于：The Annals of Probability · 年份：1974 · DOI：10.1214/aop/1176996754 · 被引用次数：39 · 研究领域：Bayesian Methods and Mixture Models、Probability and Risk Models、Statistical Methods and Inference

Wichura (1969) studied an invariance principle for partial sums of a multi-dimensional array of independent random variables. It is shown that a similar invariance principle holds for a broad class of generalized $U$-statistics for which the different terms in the partial sums are not independent. Weak convergence of generalized $U$-statistics for random sample sizes is also studied. The case of (generalized) von Mises' functional is treated briefly.