Mathematical Methods of Statistics

, Volume 23, Issue 1, pp 1–19 | Cite as

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

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.

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 

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Copyright information

© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.Laborat. Statist. et GénomeUniv. d’Évry Val d’Essonne, UMR CNRSÉvryFrance
  2. 2.Laborat. Analyse et Probab.Univ. d’Évry Val d’EssonneÉvryFrance

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