Title: Nonparametric estimation in hidden Markov models using the EM algorithm
Authors: Sina Mews - Bielefeld University (Germany) [presenting]
Roland Langrock - Bielefeld University (Germany)
Timo Adam - Bielefeld University (Germany)
Abstract: Hidden Markov models (HMMs) constitute a flexible class of models for time series data, in which the observations are generated by conditional distributions as selected by an underlying Markov chain. While the state-dependent distributions are typically assumed to be a member of some parametric family, misspecifications in this regard can lead to biased parameter estimates, to a high misclassification rate when decoding the hidden states, and to invalid inference on the number of states, to name just a few undesirable consequences. To overcome this restrictive assumption, the state-dependent distributions can be modelled nonparametrically based on penalized splines (P-splines) in order to obtain density estimates sufficiently flexible to capture any distributional shape, with a wiggliness penalty to avoid overfitting. However, parameter estimation based on numerical maximisation of the likelihood requires a computationally intensive determination of the smoothing parameters via grid search. We suggest to instead use the EM algorithm, leading to the main advantage that one can iteratively update the smoothing parameters within each M step. A simulation study as well as a real data example are used to assess the performance of the EM-based nonparametric estimation approach. Its results are compared to the numerical ML equivalent as well as to a parametric model formulation, indicating that the EM-based estimation approach is a suitable alternative to the numerical ML one.