Estimadores de máxima verossimilhança Lq para todos os parâmetros da distribuição Skew-t

Abstract

In this work, some aspects of estimation in the class of scale mixtures skew-normal distributions were taken into account, specifically in the Skew-t (ST) model. The ST distribution has interesting and important properties, such as the fact of admitting a stochastic representation that facilitates the implementation of the EM algorithm, allows combining asymmetry with heavy tails, it also has as particular cases of distributions the SkewCauchy, Skew-Normal, t-Student and normal, besides assigning different weights to each observation and consequently controlling the influence of observation in the estimation process. The parameters will be estimated using the maximum Lq-likelihood estimation method (MLq). Due to the scale mixture representation of the ST distribution, we adapted the EM algorithm for the estimators MLq for all ST model parameters, including the degrees of freedom. In addition, we discuss the robustness of this estimation method under the model of interest