Density estimation for β-dependent sequences

Abstract : We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of Rosenblatt and long-range dependent. The main probabilistic tool is a new Rosenthal-type inequality for partial sums of BV functions of the variables. As an application, we give the rates of convergence of regular Histograms, when estimating the invariant density of a class of expanding maps of the unit interval with a neutral fixed point at zero. These Histograms are plotted in the section devoted to the simulations.
Type de document :
Pré-publication, Document de travail
MAP5 2016-13. 2016
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Contributeur : Jérôme Dedecker <>
Soumis le : vendredi 13 mai 2016 - 14:45:29
Dernière modification le : jeudi 31 mai 2018 - 09:12:02
Document(s) archivé(s) le : mercredi 16 novembre 2016 - 03:41:26


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  • HAL Id : hal-01315621, version 1
  • ARXIV : 1605.05055



Jérôme Dedecker, Florence Merlevède. Density estimation for β-dependent sequences. MAP5 2016-13. 2016. 〈hal-01315621〉



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