Hidden Markov model for parameter estimation of a random walk in a Markov environment

Abstract : 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.
Complete list of metadatas

Cited literature [39 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01025035
Contributor : Catherine Matias <>
Submitted on : Friday, April 3, 2015 - 3:40:27 PM
Last modification on : Friday, May 24, 2019 - 5:26:24 PM
Long-term archiving on : Tuesday, April 18, 2017 - 9:44:34 AM

File

RW_Markov_env_Revised.pdf
Files produced by the author(s)

Identifiers

Citation

Pierre Andreoletti, Dasha Loukianova, Catherine Matias. Hidden Markov model for parameter estimation of a random walk in a Markov environment. ESAIM: Probability and Statistics, EDP Sciences, 2015, 19, pp.605 - 625. ⟨10.1051/ps/2015008⟩. ⟨hal-01025035v3⟩

Share

Metrics

Record views

979

Files downloads

222