The Annals of Probability

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

B. W. Silverman

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

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