Density estimation for $\beta$-dependent sequences
Statistics Theory
2016-05-18 v1 Statistics Theory
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.
Cite
@article{arxiv.1605.05055,
title = {Density estimation for $\beta$-dependent sequences},
author = {Jérôme Dedecker and Florence Merlevède},
journal= {arXiv preprint arXiv:1605.05055},
year = {2016}
}