Variable Selection in Composite Quantile Regression Models with Adaptive Group Lasso

Abstract

Variable selection plays an important role in the model building process. In this paper, we extend the oracle properties of adaptive group lasso penalty to the context of composite quantile regression model, simultaneously estimate regression coefficient and implement variable selection in linear regression model. By combing the information of multiple quantile regression models, we obtain the more efficient estimator of the regression coefficient compared to the standard least square estimator. In addition, we show theoretically that our proposed method is able to identify the true model consistently, and the resulting estimator can be as efficient as oracle. A real data analysis confirmed that the optimal model selected by the adaptive group lasso based on composite quantile regression procure consistently demonstrate the smallest average model size, regardless of which selection method is used.