Model Selection for High-Dimensional Quantile Regression at Multiple Percentile Levels

• Activity Number: 510
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Seyoung Park*+
• Companies: University of Michigan
• Keywords: multiple quantiles ; model selection ; high dimensional

Abstract

The penalization methods for quantile regression have been considered in the literature at a given quantile level. Belloni and Chernozhukov (2011) consider the l1-penalized quantile regression in high dimensional sparse models and obtain some non-asymptotic results. Jiang (2012) introduces a new estimator that estimates several quantiles at the same time while penalizing inter-quantile differences as well as individual quantile coefficients, but provides no theoretical results for high dimensional predictors. In this talk we consider joint quantile regression in high-dimensional sparse models by allowing the number of quantiles, K, and the number of predictors, p, to grow with the sample size n. We demonstrate the advantages of considering several quantiles together for stability and efficiency of model selection.