| Issue |
ESAIM: PS
Volume 5, 2001
|
|
|---|---|---|
| Page(s) | 51 - 76 | |
| DOI | https://doi.org/10.1051/ps:2001102 | |
| 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; prieur@math.u-cergy.fr.
Received:
19
January
2001
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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