Maximum likelihood estimator consistency for ballistic random walk in a parametric random environment

Francis Comets; Mikael Falconnet; Oleg Loukianov; Dasha Loukianova; Catherine Matias

Maximum likelihood estimator consistency for ballistic random walk in a parametric random environment

Francis Comets ¹ Mikael Falconnet ^{2, *} Oleg Loukianov ³ Dasha Loukianova ⁴ Catherine Matias ²

* Corresponding author

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

2 SG - Laboratoire Statistique et Génome

3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

4 Laboratoire Analyse et Probabilités

Abstract : We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the environment parameters based on a single observation of the path till the time it reaches a distant site, and prove that this estimator is consistent as the distant site tends to infinity. We also explore the numerical performances of our estimation procedure.

Keywords : random walk in random environment Ballistic regime maximum likelihood estimation random walk in random environment.

Document type :

Journal articles

Domain :

Mathematics [math] / Statistics [math.ST]

Statistics [stat] / Statistics Theory [stat.TH]

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https://hal.archives-ouvertes.fr/hal-00744629
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Submitted on : Wednesday, October 24, 2012 - 9:17:20 AM
Last modification on : Friday, January 4, 2019 - 5:32:33 PM
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Maximum likelihood estimator consistency for ballistic random walk in a parametric random environment

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Maximum likelihood estimator consistency for ballistic random walk in a parametric random environment

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