Bayesian mixture of parametric and nonparametric density estimation: A Misspecification Problem

In this paper we study the effect of model misspecifications for probabilitydensity function estimation. We use a mixture of a parametric and nonparametricdensity estimation. The former can be modeled by any suitable parametricprobability density function, including mixture of parametric models. The latteris given by the known B-spline estimation. The procedure also deals withthe situation when a highly structured data are collected so that it is difficultto propose a parametric model with a large number of mixture components.Then a nonparametric part would help to postulate an appropriate model. Inaddition, in order to reduce the computational cost of getting a nonparametricdensity for high dimensional data a parametric mixture of densities could beused as the starting point for modeling such dataset. Our procedure is computedby using EM-type algorithm for a non-Bayesian approach and MCMCalgorithm under a Bayesian point of view. Simulations and real data analysisshow that our proposed procedure have performed quite well even for nonstructured datasets.