Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 1, Pages 3-20
doi:10.1155/S1048953397000026

Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables

Shan Sun1 and Ching-Yuan Chiang2

1Texas Tech University, Department of Mathematics, Lubbock 79409, TX, USA
2James Madison University, Department of Mathematics, Harrisonburg 22807, VA, USA

Received 1 November 1994; Revised 1 April 1996

Copyright © 1997 Shan Sun and Ching-Yuan Chiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic Fˆn(Un) for a class of strongly mixing sequences of random variables {Xi,i≥1}. Stationarity is not assumed. Here Fˆn is the perturbed empirical distribution function and Un is a U-statistic based on X1,…,Xn.