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.
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Contributor : Jérôme Dedecker <>
Submitted on : Friday, May 13, 2016 - 2:45:29 PM
Last modification on : Friday, October 4, 2019 - 1:11:37 AM
Long-term archiving on: Wednesday, November 16, 2016 - 3:41:26 AM


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



Jérôme Dedecker, Florence Merlevède. Density estimation for β-dependent sequences. 2016. ⟨hal-01315621⟩



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