Hierarchically penalized quantile regression

Abstract

In many regression problems, predictors are naturally grouped. For example, when a set of dummy variables is used to represent categorical variables, or a set of basis functions of continuous variables is included in the predictor set, it is important to carry out a feature selection both at the group level and at individual variable levels within the group simultaneously. To incorporate the group and variables within-group information into a regularized model fitting, several regularization methods have been developed, including the Cox regression and the conditional mean regression. Complementary to earlier works, the simultaneous group and within-group variables selection method is examined in quantile regression. We propose a hierarchically penalized quantile regression, and show that the hierarchical penalty possesses the oracle property in quantile regression, as well as in the Cox regression. The proposed method is evaluated through simulation studies and a real data application.

Keywords:

• group variable selection
• hierarchical regularization
• linear programming
• quantile regression

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2A10007545) for M. Jhun and funded by the Ministry of Science, ICT and Future Planning (NRF-2013R1A1A1007536) for S. Bang.