Regularized simultaneous model selection in multiple quantiles regression

Authors:
Hui Zou;Ming Yuan
Affiliations:
University of Minnesota, United States;Georgia Institute of Technology, United States
Venue:
Computational Statistics & Data Analysis
Year:
2008

Citing 2
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Abstract

Simultaneously estimating multiple conditional quantiles is often regarded as a more appropriate regression tool than the usual conditional mean regression for exploring the stochastic relationship between the response and covariates. When multiple quantile regressions are considered, it is of great importance to share strength among them. In this paper, we propose a novel regularization method that explores the similarity among multiple quantile regressions by selecting a common subset of covariates to model multiple conditional quantiles simultaneously. The penalty we employ is a matrix norm that encourages sparsity in a column-wise fashion. We demonstrate the effectiveness of the proposed method using both simulations and an application of gene expression data analysis.