A MDL approach to HMM with Poisson and Gaussian emissions. Application to order identification
Antoine Chambaz, Aurelien Garivier and Elisabeth Gassiat
Journal of Statistical Planning and Inference 2005.

Abstract

We address the issue of order identification for HMM with Poisson and Gaussian emissions. We prove information theoretic BIC-like mixture inequalities in the spirit of (Finesso 1991), (Liu & Narayan 1994) and (Gassiat & Boucheron 2003). These inequalities lead to consistent penalized estimators that need no prior bound on the order nor on the parameters of the mixture components.

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