Empirical process of long-range dependent sequences when parameters are estimated

2007/02/05 by Kulik, Rafal
#62E20 #62F05 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.math/0702089

Abstract

In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to i.i.d. situation, as well as compared to ordinary empirical processes of long range dependent sequences. Applications include Kolmogorov-Smirnov and Cramer-Smirnov-von Mises goodness-of-fit statistics.

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