Variable selection in joint location and scale models of the skew-normal distribution

A regression model with skew-normal errors provides a useful extension for ordinary normal regression models when the data set under consideration involves asymmetric outcomes. Variable selection is an important issue in all regression analyses, and in this paper, we investigate the simultaneously variable selection in joint location and scale models of the skew-normal distribution. We propose a unified penalized likelihood method which can simultaneously select significant variables in the location and scale models. Furthermore, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the location and scale models. With appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. Simulation studies and a real example are used to illustrate the proposed methodologies.