Density Estimation for One-Dimensional Dynamical Systems

Clémentine Prieur

ESAIM: Probability and Statistics (2010)

  • Volume: 5, page 51-76
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Prieur, Clémentine. "Density Estimation for One-Dimensional Dynamical Systems." ESAIM: Probability and Statistics 5 (2010): 51-76. <http://eudml.org/doc/197744>.

@article{Prieur2010,
abstract = { 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. },
author = {Prieur, Clémentine},
journal = {ESAIM: Probability and Statistics},
keywords = {Dynamical systems; decay of correlations; invariant probability; stationary sequences; Lindeberg theorem; Central Limit Theorem; bias; nonparametric estimation; s-weakly and a-weakly dependent.},
language = {eng},
month = {3},
pages = {51-76},
publisher = {EDP Sciences},
title = {Density Estimation for One-Dimensional Dynamical Systems},
url = {http://eudml.org/doc/197744},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Prieur, Clémentine
TI - Density Estimation for One-Dimensional Dynamical Systems
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 51
EP - 76
AB - 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.
LA - eng
KW - Dynamical systems; decay of correlations; invariant probability; stationary sequences; Lindeberg theorem; Central Limit Theorem; bias; nonparametric estimation; s-weakly and a-weakly dependent.
UR - http://eudml.org/doc/197744
ER -

References

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