ESTIMATION AND ASYMPTOTIC THEORY FOR A NEW CLASS OF MIXTURE MODELS

In this paper a new model of mixture of distributions is proposed, where the mixing structure is determined by a smooth transition tree architecture. Models based on mixture of distributions are useful in order to approximate unknown conditional distributions of multivariate data. The tree structure yields a model that is simpler, and in some cases more interpretable, than previous proposals in the literature. Based on the Expectation-Maximization (EM) algorithm a quasi-maximum likelihood estimator is derived and its asymptotic properties are derived under mild regularity conditions. In addition, a specific-to-general model building strategy is proposed in order to avoid possible identification problems. Both the estimation procedure and the model building strategy are evaluated in a Monte Carlo experiment, which give strong support for the theory developed in small samples. The approximation capabilities of the model is also analyzed in a simulation experiment. Finally, two applications with real datasets are considered. KEYWORDS: Mixture models, smooth transition, EM algorithm, asymptotic properties, time series, conditional distribution.