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February, 1974 Weak Convergence of Generalized $U$-Statistics
Pranab Kumar Sen
Ann. Probab. 2(1): 90-102 (February, 1974). DOI: 10.1214/aop/1176996754

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.

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Pranab Kumar Sen. "Weak Convergence of Generalized $U$-Statistics." Ann. Probab. 2 (1) 90 - 102, February, 1974. https://doi.org/10.1214/aop/1176996754

Information

Published: February, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0276.60008
MathSciNet: MR402844
Digital Object Identifier: 10.1214/aop/1176996754

Subjects:
Primary: 60B10
Secondary: 60G99

Keywords: $D \{\lbrack 0, 1 \rbrack^c\}$ space , Gaussian processes , generalized $U$-statistics , invariance principle , random indices , relative compactness , Von Mises' differentiable statistical functions and weak convergence

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 1 • February, 1974
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