Identification and estimation of hidden Markov models

In the current thesis several selected aspects of the two related latent class models; finite mixtures and hidden Markov models, were considered. The problem of calculating the MLE of a Gaussian mixture with Newton's method and the consistency of penalized MLE were investigated. A penalized MLE procedure for univariate Gaussian hidden Markov models was introduced and shown to be consistent. Furthermore, a result on identifiability of nonparametric hidden Markov models is derived