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

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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},
     pages = {51--76},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1875664},
     zbl = {1054.60030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PS_2001__5__51_0/}
}
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%D 2001
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%F 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://geodesic.mathdoc.fr/item/PS_2001__5__51_0/