On recursive estimation for hidden Markov models

Hidden Markov models (HMMs) have during the last decade become a widespread tool for modelling sequences of dependent random variables. In this paper we consider a recursive estimator for HMMs based on the m-dimensional distribution of the process and show that this estimator converges to the set of stationary points of the corresponding Kullback-Leibler information. We also investigate averaging in this recursive scheme and show that conditional on convergence to the true parameter, and provided m is chosen large enough, the averaged estimator is close to optimal.