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Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonallong-memory

Published online by Cambridge University Press:  15 November 2002

Mohamedou Ould Haye
Mohamedou Ould Haye*
Affiliation:
Laboratoire de Statistique et Probabilités, bâtiment M2, FRE 2222 du CNRS, Université des Sciences et Technologies de Lille, 59655 Villeneuve-d'Ascq Cedex, France; ouldmoha@jacta.univ-lille1.fr.
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Abstract

We study the asymptotic behavior of the empirical process when theunderlying data are Gaussian and exhibit seasonallong-memory. We prove that the limiting process can be quitedifferent from the limit obtained in the case of regularlong-memory. However, in both cases, the limiting process isdegenerated. We apply our results to von–Mises functionals andU-Statistics.

Keywords

Empirical processHermite polynomialsRosenblatt processesseasonal long-memoryU-statisticsvon–Mises functionals.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 293 - 309
Copyright
© EDP Sciences, SMAI, 2002

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