Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables. (1997)

• Record Type: Journal Article
• Authors: Sun, Shan; Chiang, Ching-Yuan
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 10:Number 1(1997)
• Page Start: 3
• Page End: 20
• Publication Date: 1997
• Subjects: perturbed empirical distribution functions -- strong mixing -- almost sure representation -- U-statistic -- law of the iterated logarithm -- invariance principle; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953397000026
• Languages: English
• ISSNs: 1048-9533

Abstract

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