Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 1, Pages 3-20
Limiting behavior of the perturbed empirical distribution functions evaluated at -statistics for strongly mixing sequences of random variables
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.
We prove the almost sure representation, a law of the iterated logarithm
and an invariance principle for the statistic for a class of strongly
mixing sequences of random variables . Stationarity is not
assumed. Here is the perturbed empirical distribution function and
is a -statistic based on .