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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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
- 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