An Efficient Calculation of the Moments of Matched and Mismatched Hidden Markov Models

Streit analysed the classification of an unknown hidden Markov model (HMM) using a set of prescribed HMM’s. He proposed a suboptimal test statistic that can be approximated by certain moments for this classification. In this correspondence, the algorithm given by Streit to derive these moments is reformulated in a matrix algebra setting that gives a better insight into the algorithm. Also, an asymptotic analysis of the algorithm is derived using the reformulation.