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Density Estimation for One-Dimensional Dynamical Systems

Published online by Cambridge University Press:  15 August 2002

Clémentine Prieur
Clémentine Prieur*
Affiliation:
Université de Cergy-Pontoise, Laboratoire de Mathématiques, bâtiment A4, Site Saint-Martin, 95011 Cergy-Pontoise Cedex, France; prieur@math.u-cergy.fr.
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Abstract

In this paper we prove a Central Limit Theorem forstandard kernel estimates of the invariant density of one-dimensionaldynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergencefor the variance of the estimator and a variation on the Lindeberg–Riomethod. We also give an extension in the case of weaklydependent sequences in a sense introduced by Doukhan and Louhichi.

Keywords

Dynamical systemsdecay of correlationsinvariant probabilitystationary sequencesLindeberg theoremCentral Limit Theorembiasnonparametric estimations-weakly and a-weakly dependent.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 5 , 2001 , pp. 51 - 76
Copyright
© EDP Sciences, SMAI, 2001

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