We focus on the parametric estimation of the distribution of a Markov environment from the observation of a single trajectory of a one-dimensional nearest-neighbor path evolving in this random environment. In the ballistic case, as the length of the path increases, we prove consistency, asymptotic normality and efficiency of the maximum likelihood estimator. Our contribution is two-fold: we cast the problem into the one of parameter estimation in a hidden Markov model (HMM) and establish that the bivariate Markov chain underlying this HMM is positive Harris recurrent. We provide different examples of setups in which our results apply, in particular that of DNA unzipping model, and we give a simple synthetic experiment to illustrate those results.
DOI : 10.1051/ps/2015008
Mots-clés : Hidden Markov model, Markov environment, maximum likelihood estimation, random walk in random environment
@article{PS_2015__19__605_0,
author = {Andreoletti, Pierre and Loukianova, Dasha and Matias, Catherine},
title = {Hidden {Markov} model for parameter estimation of a random walk in a {Markov} environment},
journal = {ESAIM: Probability and Statistics},
pages = {605--625},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2015008},
mrnumber = {3433429},
zbl = {1392.62246},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2015008/}
}
TY - JOUR AU - Andreoletti, Pierre AU - Loukianova, Dasha AU - Matias, Catherine TI - Hidden Markov model for parameter estimation of a random walk in a Markov environment JO - ESAIM: Probability and Statistics PY - 2015 SP - 605 EP - 625 VL - 19 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2015008/ DO - 10.1051/ps/2015008 LA - en ID - PS_2015__19__605_0 ER -
%0 Journal Article %A Andreoletti, Pierre %A Loukianova, Dasha %A Matias, Catherine %T Hidden Markov model for parameter estimation of a random walk in a Markov environment %J ESAIM: Probability and Statistics %D 2015 %P 605-625 %V 19 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2015008/ %R 10.1051/ps/2015008 %G en %F PS_2015__19__605_0
Andreoletti, Pierre; Loukianova, Dasha; Matias, Catherine. Hidden Markov model for parameter estimation of a random walk in a Markov environment. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 605-625. doi : 10.1051/ps/2015008. http://www.numdam.org/articles/10.1051/ps/2015008/
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