Abstract
We study the ${\mathbb{L}}^{p}$-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.
Citation
Jérôme Dedecker. Florence Merlevède. "Density estimation for $\tilde{\beta}$-dependent sequences." Electron. J. Statist. 11 (1) 981 - 1021, 2017. https://doi.org/10.1214/17-EJS1249
Information