New methods for the statistical analysis of Hidden Markov Models

The estimation of Hidden Markov Models has attracted a lot of attention recently. The purpose of this paper is to lay the foundation for a new approach for the analysis of the maximum-likelihood estimation of HMM-s, using representation of HMM-s due to Borkar (1993). A useful connection between the estimation theory of HMM-s and linear stochastic systems is established via the theory of L-mixing processes. The results are potentially useful for deriving strong approximation results, which are in turn applicable to analyze adaptive predictors and change detection methods.