Multitask Quantile Regression Under the Transnormal Model

Jianqing Fan, Lingzhou Xue, Hui Zou

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We consider estimating multitask quantile regression under the transnormal model, with focus on high-dimensional setting. We derive a surprisingly simple closed-form solution through rank-based covariance regularization. In particular, we propose the rank-based ℓ1 penalization with positive-definite constraints for estimating sparse covariance matrices, and the rank-based banded Cholesky decomposition regularization for estimating banded precision matrices. By taking advantage of the alternating direction method of multipliers, nearest correlation matrix projection is introduced that inherits sampling properties of the unprojected one. Our work combines strengths of quantile regression and rank-based covariance regularization to simultaneously deal with nonlinearity and nonnormality for high-dimensional regression. Furthermore, the proposed method strikes a good balance between robustness and efficiency, achieves the “oracle”-like convergence rate, and provides the provable prediction interval under the high-dimensional setting. The finite-sample performance of the proposed method is also examined. The performance of our proposed rank-based method is demonstrated in a real application to analyze the protein mass spectroscopy data. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1726-1735
Number of pages10
JournalJournal of the American Statistical Association
Volume111
Issue number516
DOIs
StatePublished - Oct 1 2016

Keywords

  • Alternating direction method of multipliers
  • Cholesky decomposition
  • Copula model
  • Optimal transformation
  • Prediction interval
  • Quantile regression
  • Rank correlation

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