Density estimation for one-dimensional dynamical systems
ESAIM: Probability and Statistics, Volume 5  (2001), p. 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
@article{PS_2001__5__51_0,
     author = {Prieur, Cl\'ementine},
     title = {Density estimation for one-dimensional dynamical systems},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     pages = {51-76},
     zbl = {1054.60030},
     mrnumber = {1875664},
     language = {en},
     url = {http://www.numdam.org/item/PS_2001__5__51_0}
}
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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