Open Access
December 2009 Subspace estimation and prediction methods for hidden Markov models
Sofia Andersson, Tobias Rydén
Ann. Statist. 37(6B): 4131-4152 (December 2009). DOI: 10.1214/09-AOS711


Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite set as well. In particular, we study the geometric structure arising from the nonminimality of the linear state space representation of HMMs, and consistency of a subspace algorithm arising from a certain factorization of the singular value decomposition of the estimated linear prediction matrix. For this algorithm, we show that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation, and that the m-step linear predictor computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear m-step predictor.


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Sofia Andersson. Tobias Rydén. "Subspace estimation and prediction methods for hidden Markov models." Ann. Statist. 37 (6B) 4131 - 4152, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1191.62141
MathSciNet: MR2572455
Digital Object Identifier: 10.1214/09-AOS711

Primary: 62M09
Secondary: 62M10 , 62M20 , 93B15 , 93B30

Keywords: consistency , Hidden Markov model , linear innovation representation , prediction error representation , subspace estimation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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