2016/05/17 by Jérôme Dedecker, Dedecker, Jérôme, Florence Merlevède +1
Mathematics · #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Dynamics and Fractals #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1605.05055
openalex publication_date 2016/05/17 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
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.