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1 MAP5 - MAP5 - Mathématiques Appliquées à Paris 5 2 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées

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.

Keywords : long-range dependence density estimation stationary processes expanding maps

Author: Jérôme Dedecker - Florence Merlevède -



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