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Théorèmes limites pour des processus à longue mémoire saisonnière

Abstract : We study the asymptotic behavior of statistics or functionals based on seasonal long-memory processes. We focus on the Donsker-line and on the empirical process for two large classes~: the subordinated Gaussian sequences and the linear processes. Twenty five years ago, Taqqu and Dobrushin and Major obtained fundamental results for processes having a regular varying covariance. We prove that these results may no longer hold when seasonal effects are incorporated. The modifications concern the normalizing coefficient as well the type of the limit process. For example we prove that the limit of the doubly indexed empirical process is no more induced by the Hermite rank of the basic distribution function. More particularly, when the Hermite rank is one, this limit is not necessarily Gaussian. For instance we can obtain a linear combination of independent Rosenblatt processes. Connected statistical problems are considered~: limit behavior of U-statistics, density estimation and testing for change point.
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https://tel.archives-ouvertes.fr/tel-00001326
Contributor : Mohamedou Ould Haye <>
Submitted on : Sunday, April 28, 2002 - 12:50:15 PM
Last modification on : Thursday, February 21, 2019 - 10:34:03 AM
Long-term archiving on: : Tuesday, September 11, 2012 - 5:20:19 PM

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Mohamedou Ould Mohamed Abdel Haye. Théorèmes limites pour des processus à longue mémoire saisonnière. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 2001. Français. ⟨tel-00001326⟩

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