We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove that the maximum likelihood and a quasi-maximum likelihood estimator (QMLE) are strongly consistent. The computation of the QMLE ignores the inhomogeneity, hence, is much simpler and robust. The theory is motivated by an example from biophysics and applied to a Poisson- and linear Gaussian model.
Accepté le :
DOI : 10.1051/ps/2018017
Mots-clés : Inhomogeneous hidden Markov models, quasi-maximum likelihood estimation, strong consistency, robustness, asymptotic mean stationarity
@article{PS_2019__23__492_0,
author = {Diehn, Manuel and Munk, Axel and Rudolf, Daniel},
title = {Maximum likelihood estimation in hidden {Markov} models with inhomogeneous noise},
journal = {ESAIM: Probability and Statistics},
pages = {492--523},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2018017},
mrnumber = {3989601},
zbl = {1422.62099},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2018017/}
}
TY - JOUR AU - Diehn, Manuel AU - Munk, Axel AU - Rudolf, Daniel TI - Maximum likelihood estimation in hidden Markov models with inhomogeneous noise JO - ESAIM: Probability and Statistics PY - 2019 SP - 492 EP - 523 VL - 23 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2018017/ DO - 10.1051/ps/2018017 LA - en ID - PS_2019__23__492_0 ER -
%0 Journal Article %A Diehn, Manuel %A Munk, Axel %A Rudolf, Daniel %T Maximum likelihood estimation in hidden Markov models with inhomogeneous noise %J ESAIM: Probability and Statistics %D 2019 %P 492-523 %V 23 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2018017/ %R 10.1051/ps/2018017 %G en %F PS_2019__23__492_0
Diehn, Manuel; Munk, Axel; Rudolf, Daniel. Maximum likelihood estimation in hidden Markov models with inhomogeneous noise. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 492-523. doi : 10.1051/ps/2018017. http://www.numdam.org/articles/10.1051/ps/2018017/
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