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Article Dans Une Revue Stochastic Processes and their Applications Année : 2016

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

Résumé

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.

Dates et versions

hal-02631186 , version 1 (27-05-2020)

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Francis Comets, Mikael Falconnet, Oleg Loukianov, Dasha Loukianova. Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support. Stochastic Processes and their Applications, 2016, 126 (11), pp.3578-3604. ⟨10.1016/j.spa.2016.04.034⟩. ⟨hal-02631186⟩
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