Density estimation for one-dimensional dynamical systems
ESAIM: Probability and Statistics, Volume 5 (2001), pp. 51-76.

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.

Classification: 37D20,  37M10,  37A50,  60G07,  60G10
Keywords: dynamical systems, decay of correlations, invariant probability, stationary sequences, Lindeberg theorem, central limit theorem, bias, nonparametric estimation, $s$-weakly and $a$-weakly dependent
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author = {Prieur, Cl\'ementine},
title = {Density estimation for one-dimensional dynamical systems},
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url = {http://www.numdam.org/item/PS_2001__5__51_0/}
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Prieur, Clémentine. Density estimation for one-dimensional dynamical systems. ESAIM: Probability and Statistics, Volume 5 (2001), pp. 51-76. http://www.numdam.org/item/PS_2001__5__51_0/

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