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Density Estimation for One-Dimensional Dynamical Systems

Published online by Cambridge University Press:  15 August 2002

Clémentine Prieur*
Université de Cergy-Pontoise, Laboratoire de Mathématiques, bâtiment A4, Site Saint-Martin, 95011 Cergy-Pontoise Cedex, France;
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In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.

Research Article
© EDP Sciences, SMAI, 2001

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