Regularized simultaneous model selection in multiple quantiles regression

Hui Zou, Ming Yuan

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)5296-5304
Number of pages9
JournalComputational Statistics and Data Analysis
Volume52
Issue number12
DOIs
StatePublished - Aug 15 2008

Bibliographical note

Funding Information:
We thank Professor Mark Segal for kindly providing us the cardiomypathy data. The authors sincerely thank an AE and two referees for their helpful comments that substantially improved an earlier version of this paper. This work is supported by NSF grant DMS-0706733.

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