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

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

2007-02-05

arxiv.org/abs/math/0702089v1

Mathematics

Statistics Theory

12 pages

Scientific paper

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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