Non parametric estimation for random walks in random environment

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Diel, Roland¹  Lerasle, Matthieu¹ 

[1] Univ Cote Azur, CNRS, LJAD, Nice, France

关键词: Random walk in random environment;    Non-parametric estimation;    Oracle inequalities;    Adaptive estimation;   

DOI  :  10.1016/j.spa.2017.04.011

来源: Elsevier

【 摘 要 】

We investigate the problem of estimating the cumulative distribution function (c.d.f.) F of a distribution nu from the observation of one trajectory of the random walk in i.i.d. random environment with distribution nu on Z. We first estimate the moments of nu, then combine these moment estimators to obtain a collection of estimators ((F) over cap (M)(n))(m >= 1) of F, our final estimator is chosen among this collection by Goldenshluger-Lepski's method. This estimator is easily computable. We derive convergence rates for this estimator depending on the Holder regularity of F and on the divergence rate of the walk. Our rate is minimal when the chain realizes a trade-off between a fast exploration of the sites, allowing to get more information and a larger number of visits of each site, allowing a better recovery of the environment itself. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free