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Article Dans Une Revue Electronic Journal of Statistics Année : 2017

Density estimation for β-dependent sequences

Résumé

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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Dates et versions

hal-01315621 , version 1 (13-05-2016)

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Jérôme Dedecker, Florence Merlevède. Density estimation for β-dependent sequences. Electronic Journal of Statistics , 2017, 11 (1), ⟨10.1214/17-EJS1249⟩. ⟨hal-01315621⟩
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