Asymptotic normality and efficiency of the maximum likelihood estimator for the parameter of a ballistic random walk in a random environment

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 an asymptotic normality result 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 behaviour of asymptotic confidence regions for the parameter value.
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Mikael Falconnet, Dasha Loukianova, Catherine Matias. Asymptotic normality and efficiency of the maximum likelihood estimator for the parameter of a ballistic random walk in a random environment. Mathematical Methods of Statistics, Allerton Press, Springer (link), 2014, 23 (1), pp.1-19. ⟨10.3103/S1066530714010013⟩. ⟨hal-00783980v2⟩

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