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

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.