The Annals of Probability

Functional Limit Theorems for $U$-Processes

Deborah Nolan and David Pollard

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Abstract

A $U$-process is a collection of $U$-statistics indexed by a family of symmetric kernels. In this paper, two functional limit theorems are obtained for sequences of standardized $U$-processes. In one case the limit process is Gaussian; in the other, the limit process has finite dimensional distributions of infinite weighted sums of $\chi^2$ random variables. Goodness-of-fit statistics provide examples.

Article information

Source
Ann. Probab., Volume 16, Number 3 (1988), 1291-1298.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991691

Digital Object Identifier
doi:10.1214/aop/1176991691

Mathematical Reviews number (MathSciNet)
MR942769

Zentralblatt MATH identifier
0665.60037

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62E20: Asymptotic distribution theory

Keywords
$U$-statistics empirical processes functional limit theorems equicontinuity finite dimensional distributions goodness-of-fit statistics

Citation

Nolan, Deborah; Pollard, David. Functional Limit Theorems for $U$-Processes. Ann. Probab. 16 (1988), no. 3, 1291--1298. doi:10.1214/aop/1176991691. https://projecteuclid.org/euclid.aop/1176991691


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