Asymptotic properties of the maximum likelihood estimation in misspecified Hidden Markov models

Details Asymptotic properties of the maximum likelihood estimation in misspecified Hidden Markov models Asymptotic properties of the maximum likelihood estimation in misspecified Hidden Markov models

2011-10-03

arxiv.org/abs/1110.0356v1

Mathematics

Statistics Theory

Scientific paper

Let $(Y_k)$ be a stationary sequence on a probability space taking values in a standard Borel space. Consider the associated maximum likelihood estimator with respect to a parametrized family of Hidden Markov models such that the law of the observations $(Y_k)$ is not assumed to be described by any of the Hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such mispecified models under mild assumptions.

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