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Wavelet-based method for nonparametric estimation of HMMs

In this letter, we propose a new algorithm for nonparametric estimation of hidden Markov models (HMM's). The algorithm is based on a "wavelet-shrinkage" density estimator for the state-conditional probability density functions of the HMMs. It operates in an iterative fashion similar to that of the EM reestimation formulae used for maximum likelihood estimation of parametric HMM's. We apply the resulting algorithm to simple examples and show its convergence. The proposed method is also compared to classical nonparametric HMM estimation based on quantization of observations ("histograms") and discrete HMM's.