Variable Selection in Heteroscedastic Regression Models Under General Skew-t Distributional Models Using Information Complexity

Abstract

In this paper we study several competing models under general class of skew-t distributions. Namely. we consider joint location and scale model (JLSM) under Student’s t and under skew-t distributions, respectively. Similarly, we consider the extension of JLSM to joint location-scale and skewness model (JLSSM) under skew-t distribution in heteroscedastic regression models for subset selection of variables and to deal with heavy-tailedness, and skewness in a data set. To this end, for the first time, we introduce and develop the information-theoretic measure of complexity (ICOMP) criterion in such problems to select the best subset of predictor variables. We provide the computational forms of the celebrated Fisher information and the inverse Fisher information matrices for these models to be used in ICOMP. A large-scale Monte Carlo simulation study is carried out to study the performance of ICOMP in such complicated models. In addition, a real example is provided on a real benchmark data set to select the best subset of the predictors under these three competing models without knowing the true structure and the distributional form of the regression model. Our approach shows the flexibility and versatility of our approach for model selection in complex models.