Seminarium i matematisk statistik
torsdagen den 13 januari 13.15 i MH:228

Randal Douc

Ecole Nationale Supérieure des Télécommunications,
Paris

Titel:
Asymptotics of the Maximum Likelihood Estimator 
for general Hidden Markov Models

Abstract:
Hidden Markov Models form a wide class of discrete-time stochastic
processes, used in different areas such as speech recognition, biology,
econometrics or time series analysis. In our work, we consider the
consistency and asymptotic normality of the maximum likelihood estimator
for a possibly non-stationary Hidden Markov Model where the hidden state
space is a compact set, non necessarily finite, and both the transition
kernel of the hidden chain and the conditional distribution of the
observations depend on a parameter. For identifiable models, consistency
and asymptotic normality of the maximum likelihood estimator is shown to
follow from exponential forgetting properties of the state prediction
filter and geometric ergodicity of suitably extended Markov chains.