Variable selection in joint location, scale and skewness models with a skew-t-normal distribution

Although there are many papers on variable selection methods in the modeling of the mean and/or variance parameters, little work has been done on how to select significant explanatory variables in the modeling of the skewness parameter. In this article, we propose a unified penalized likelihood method to simultaneously select significant variables and estimate unknown parameters in a joint location, scale and skewness model with a skew-t-normal (StN) distribution when outliers and asymmetrical outcomes are present. With an appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. Simulation studies are conducted to assess the finite sample performance of the proposed variable selection procedure. A real example is used to illustrate the proposed method.