Dantzig-Type Penalization for Multiple Quantile Regression with High-Dimensional Covariates

• Activity Number: 126
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Seyoung Park* and Xuming He and Shuheng Zhou
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Quantile regression ; Multiple quantiles ; Model selection ; Fused lasso ; Stability ; High dimensional data

Abstract

We study joint quantile regression at multiple quantile levels with high dimensional covariates. Variable selection performed at individual quantile levels may lack stability across quantiles, making it difficult to understand and interpret the impact of a given covariate on the conditional quantile functions. We propose a Dantzig-type penalization method for sparse model selection at each quantile level which at the same time aims to shrink the differences of the selected models across neighboring quantiles. We establish an asymptotic property of model selection consistency, and investigate the stability of the selected models across quantiles. The numerical examples and the real data analysis demonstrate that our Dantzig-type quantile regression model selection method provides stable results by reducing the noisy components of usual model selection performed at individual quantile levels.