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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 volume 23, pages 1–19 (2014)Cite this article

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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Authors and Affiliations

  1. Laborat. Statist. et Génome, Univ. d’Évry Val d’Essonne, UMR CNRS, Évry, 8071, France

    M. Falconnet & C. Matias

  2. Laborat. Analyse et Probab., Univ. d’Évry Val d’Essonne, Évry, France

    D. Loukianova

Authors
  1. M. Falconnet
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  2. D. Loukianova
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  3. C. Matias
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Correspondence to M. Falconnet.

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Falconnet, M., Loukianova, D. & Matias, C. Asymptotic normality and efficiency of the maximum likelihood estimator for the parameter of a ballistic random walk in a random environment. Math. Meth. Stat. 23, 1–19 (2014). https://doi.org/10.3103/S1066530714010013

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  • DOI: https://doi.org/10.3103/S1066530714010013

Keywords

  • asymptotic normality
  • ballistic random walk
  • confidence regions
  • Cramér-Rao efficiency
  • maximum likelihood estimation
  • random walk in random environment

2000 Mathematics Subject Classification

  • primary 62M05, 62F12
  • secondary 60J25