The Annals of Probability

Weak Convergence of Generalized $U$-Statistics

Pranab Kumar Sen

Abstract

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.

Article information

Source
Ann. Probab., Volume 2, Number 1 (1974), 90-102.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996754

Digital Object Identifier
doi:10.1214/aop/1176996754

Mathematical Reviews number (MathSciNet)
MR402844

Zentralblatt MATH identifier
0276.60008

JSTOR
Sen, Pranab Kumar. Weak Convergence of Generalized $U$-Statistics. Ann. Probab. 2 (1974), no. 1, 90--102. doi:10.1214/aop/1176996754. https://projecteuclid.org/euclid.aop/1176996754