Asymptotic normality and efficiency of the maximum likelihood estimator for the parameter of a ballistic random walk in a random environment |
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Authors: | M. Falconnet D. Loukianova C. Matias |
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Affiliation: | 1. Laborat. Statist. et Génome, Univ. d’évry Val d’Essonne, UMR CNRS, évry, 8071, France 2. Laborat. Analyse et Probab., Univ. d’évry Val d’Essonne, évry, France
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Abstract: | We consider a one-dimensional ballistic random walk evolving in a parametric independent and identically distributed random environment. We study the asymptotic properties of the maximum likelihood estimator of the parameter based on a single observation of the path till the time it reaches a distant site. We prove asymptotic normality for this consistent estimator as the distant site tends to infinity and establish that it achieves the Cramér-Rao bound. We also explore in a simulation setting the numerical behavior of asymptotic confidence regions for the parameter value. |
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