Semiparametric Hidden Markov Models
Jörn Dannemann · Journal of Computational and Graphical Statistics · 2012
Hidden Markov models (HMMs) are widely used for dependent data modeling. Classically, the state-dependent distributions, that is, the distribution of the observation given the hidden state, belong to some parametric family. This article proposes a semiparametric HMM for continuous observations with at least one state-dependent distribution modeled with modern nonparametric techniques, for example, nonparametric maximum likelihood estimation under shape constraints like log-concavity. The resulting model is much more flexible and avoids a model misspecification bias. Concentrating on the special case of two states, the article discusses identifiability of the model. Further, an estimation procedure for semiparametric HMMs is proposed based on the expectation–maximization algorithm, which gives also rise to model validation techniques, as demonstrated in a simulation study and an empirical illustration.