Density estimation for RWRE
Statistics Theory
2018-06-18 v1 Statistics Theory
Abstract
We consider the problem of non-parametric density estimation of a random environment from the observation of a single trajectory of a random walk in this environment. We first construct a density estimator using the beta-moments. We then show that the Goldenshluger-Lepski method can be used to select the beta-moment. We prove non-asymptotic bounds for the supremum norm of these estimators for both the recurrent and the transient to the right cases. A simulation study supports our theoretical findings.
Keywords
Cite
@article{arxiv.1806.05839,
title = {Density estimation for RWRE},
author = {Antoine Havet and Matthieu Lerasle and Éric Moulines},
journal= {arXiv preprint arXiv:1806.05839},
year = {2018}
}