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invariant probability

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1 results

Density Estimation for One-Dimensional Dynamical Systems
Clémentine Prieur
Journal:

ESAIM: Probability and Statistics / Volume 5 / 2001

Published online by Cambridge University Press:

15 August 2002, pp. 51-76

Print publication:

2001
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In this paper we prove a Central Limit Theorem forstandard kernel estimates of the invariant density of one-dimensionaldynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergencefor the variance of the estimator and a variation on the Lindeberg–Riomethod. We also give an extension in the case of weaklydependent sequences in a sense introduced by Doukhan and Louhichi.