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.
Mots clés : dynamical systems, decay of correlations, invariant probability, stationary sequences, Lindeberg theorem, central limit theorem, bias, nonparametric estimation, $s$-weakly and $a$-weakly dependent
@article{PS_2001__5__51_0,
author = {Prieur, Cl\'ementine},
title = {Density estimation for one-dimensional dynamical systems},
journal = {ESAIM: Probability and Statistics},
pages = {51--76},
publisher = {EDP-Sciences},
volume = {5},
year = {2001},
mrnumber = {1875664},
zbl = {1054.60030},
language = {en},
url = {http://archive.numdam.org/item/PS_2001__5__51_0/}
}
Prieur, Clémentine. Density estimation for one-dimensional dynamical systems. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 51-76. http://archive.numdam.org/item/PS_2001__5__51_0/
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