A stochastic approximation ECME algorithm to semi-parametric scale mixtures of centred skew normal regression models

In many situations we are interested in modeling data where there is no a clear relationship between the response and the covariates. In the literature there are few related proposals based on the additive partially linear models and normal distribution. It is also common to find situations where the response distribution, even conditionally on the covariates, presents asymmetry and/or heavy tails. In these situations it is more suitable to consider models based on the general class of scale mixture of skew-normal distributions, mainly under the respective centered reparameterization, due to the some inferential issues. In this paper, we developed a class of additive partially linear models based on scale mixture of skew-normal under the centered parameterization. We explore a hierarchical representation and set up an algorithm for maximum likelihood estimation based on the stochastic-approximation-expectation-maximization and expectation-conditional-maximization-either algorithms. A Monte Carlo experiment is conducted to evaluate the performance of these estimators in small and moderate samples. Furthermore, we developed residuals and influence diagnostic tools. The methodology is illustrated with the analysis of a real data set.