Weak Convergence of Generalized $U$-Statistics

Open Access

1 February 1974

journal article
Published by Institute of Mathematical Statistics in The Annals of Probability

Vol. 2 (1) , 90-102
https://doi.org/10.1214/aop/1176996754

Abstract

Wichura (1969) has 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' functionals is treated briefly.

Keywords

DCO
GENERALIZED U-STATISTICS
RANDOM INDICES AND WEAK CONVERGENCE.
RELATIVE COMPACTNESS
GAUSSIAN PROCESSES
L SPACE
INVARIANCE PRINCIPLE
RANDOM SAMPLING
PARTIAL SUMS
GAUSSIAN PROCESS
WEAK CONVERGENCE

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