Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Comets, Francis¹  Falconnet, Mikael²  Loukianov, Oleg^2,3  Loukianova, Dasha² 

[1] Univ Paris Diderot, UMR CNRS 7599, Lab Probabilites & Modeles Aleatoires, F-75205 Paris 13, France

[2] Univ Evry Val dEssonne, Lab Math & Modelisat Evry, UMR CNRS 8071, USC INRA, 23 Blvd France, F-91037 Evry, France

[3] Univ Paris Est, IUT Fontainebleau, F-77300 Fontainebleau, France

关键词: Recurrent regime;    Maximum likelihood estimation;    Random walk in random environment;   

DOI  :  10.1016/j.spa.2016.04.034

来源: Elsevier

【 摘 要 】

We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood estimation procedure of the parameters of the environment. Unlike most of the classical maximum likelihood approach, the limit of the criterion function is in general a non degenerate random variable and convergence does not hold in probability. Not only the leading term but also the second order asymptotic is needed to fully identify the unknown parameter. We present different frameworks to illustrate these facts. We also explore the numerical performance of our estimation procedure. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free