Density Estimation for One-Dimensional Dynamical Systems
ESAIM: Probability and Statistics (2010)
- Volume: 5, page 51-76
- ISSN: 1292-8100
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topPrieur, 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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