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

Rafal Kulik

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

Rafal Kulik

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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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Rafal Kulik. 2007-02-05. Empirical process of long-range dependent sequences when parameters are estimated. https://arxiv.org/abs/math/0702089

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