Efficient importance sampling in mixture frameworks

A flexible importance sampling procedure for the likelihood evaluation of dynamic latent variable models involving mixtures of distributions leading to possibly heavy tailed or multi-modal target densities is provided. The procedure is based upon the efficient importance sampling (EIS) approach and exploits the mixture structure of the model via data augmentation when constructing importance sampling distributions as mixtures of distributions. The proposed mixture EIS procedure is illustrated with ML estimation of a Student-t state space model for realized volatilities. MC simulations are used to characterize the sampling distribution of the ML estimator based upon the mixture EIS approach.