A general robust approach for joint modeling of the family of scale mixture of Normal distribution

In this paper, we present the class of linear models with errors belonging to the family of scale mixture of normal distributions, considering the reparameterization of the scatter matrix based on the Modified Cholesky Decomposition approach and that the mixing parameters of the model are deterministic but unknown and vary from each observation. Scoring functions and Hessian matrices are derived for the parameters of interest and an iterative process is proposed for parameter estimation. Some aspects of predicting new observations and robustness of maximum likelihood estimates are discussed, as well as the performance of different models with different structures for one of the parameters of the family of distributions used. The methodology is applied in an extensive comparative approach with synthetic and real data. Performance results and prediction of new observations show that the proposed model performs better compared to recent models based on Normal, Student-t and Laplace distributions.