Volume 5, 2001
|Page(s)||51 - 76|
|Published online||15 August 2002|
Density Estimation for One-Dimensional Dynamical Systems
Université de Cergy-Pontoise,
Laboratoire de Mathématiques, bâtiment A4, Site Saint-Martin,
95011 Cergy-Pontoise Cedex, France; firstname.lastname@example.org.
Revised: 9 March 2001
Revised: 12 June 2001
Revised: 3 July 2001
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.
Mathematics Subject Classification: 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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