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Issue ESAIM: PS
Volume 5, 2001
Page(s) 51 - 76
DOI 10.1051/ps:2001102

DOI: 10.1051/ps:2001102


ESAIM: P&S, September 2001, Vol. 5, pp. 51-76

Density Estimation for One-Dimensional Dynamical Systems

Clémentine Prieur

Université de Cergy-Pontoise, Laboratoire de Mathématiques, bâtiment A4, Site Saint-Martin, 95011 Cergy-Pontoise Cedex, France; (prieur@math.u-cergy.fr)

(Received January 19, 2001. Revised March 9, June 12 and July 3, 2001.)

Abstract
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.


AMS Subject: 37D20, 37M10, 37A50, 60G07, 60G10.

Key words: Dynamical systems, decay of correlations, invariant probability, stationary sequences, Lindeberg theorem, Central Limit Theorem, bias, nonparametric estimation, s-weakly and a-weakly dependent.


© EDP Sciences, SMAI 2001


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