New estimation in mixture of experts models using the Pearson type VII distribution

Abstract

Assuming that the error terms follow a Pearson type VII distribution, we propose a new estimation in mixture of experts models by adding an norm of the regression coefficients of the mixing proportions to the log-likelihood function. This l2-penalized maximum likelihood estimator is a root-n consistent estimator of the true parameter vector, and its finite sample behaviour is better than that of the ordinary maximum likelihood estimator. An efficient EM algorithm is suggested for the inference, and the methodology is illustrated through some simulation and comparison studies. An application of the proposed method to a data set is described.