Maximum likelihood estimation in hidden Markov models with inhomogeneous noise

TL;DR

This paper proves the strong consistency of maximum likelihood and quasi-maximum likelihood estimators in hidden Markov models with time-dependent inhomogeneous noise, simplifying computation and ensuring robustness, with applications in biophysics.

Contribution

It introduces a robust QMLE approach for hidden Markov models with inhomogeneous noise, proving its strong consistency under certain conditions.

Findings

QMLE ignores inhomogeneity for simplicity

QMLE is strongly consistent in the specified models

Application demonstrated in biophysical models

Abstract

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.