The Annals of Probability

Convergence of a Class of Empirical Distribution Functions of Dependent Random Variables

B. W. Silverman

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Abstract

A class of empirical processes having the structure of $U$-statistics is considered. The weak convergence of the processes to a continuous Gaussian process is proved in weighted sup-norm metrics stronger than the uniform topology. As an application, a central limit theorem is derived for a very general class of non-parametric statistics.

Article information

Source
Ann. Probab., Volume 11, Number 3 (1983), 745-751.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993518

Digital Object Identifier
doi:10.1214/aop/1176993518

Mathematical Reviews number (MathSciNet)
MR704560

Zentralblatt MATH identifier
0514.60040

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 62E20: Asymptotic distribution theory 62G80

Keywords
Weak convergence sup-norm metrics empirical process dissociated random variables $U$-statistics order statistics $GL$-statistics asymptotic normality

Citation

Silverman, B. W. Convergence of a Class of Empirical Distribution Functions of Dependent Random Variables. Ann. Probab. 11 (1983), no. 3, 745--751. doi:10.1214/aop/1176993518. https://projecteuclid.org/euclid.aop/1176993518


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