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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.
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.
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