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




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Journal of Applied Mathematics and Stochastic Analysis - Volume 10 1997, Issue 1, Pages 3-20



Texas Tech University, Department of Mathematics, Lubbock 79409, TX, USA

James Madison University, Department of Mathematics, Harrisonburg 22807, VA, USA

Received 1 November 1994; Revised 1 April 1996

Copyright © 1997 Hindawi Publishing Corporation. 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 FˆnUn 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 Unis a U-statistic based on X1,…,Xn.





Author: Shan Sun and Ching-Yuan Chiang

Source: https://www.hindawi.com/



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