Maximum-likelihood estimation for mixture multivariate stochastic observations of Markov chains

In this paper we discuss parameter estimation by means of the reestimation algorithm for a class of multivariate mixture density functions of Markov chains. The scope of the original reestimation algorithm is expanded and the previous assumptions of log concavity or ellipsoidal symmetry are obviated, thereby enhancing the modeling capability of the technique. Reestimation formulas in terms of the well-known forward-backward inductive procedure are also derived.