Multitask Quantile Regression Under the Transnormal Model

Jianqing Fan, Lingzhou Xue, Hui Zou

Research output: Contribution to journalArticle

8 Citations (Scopus)

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

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Quantile Regression
Regularization
High-dimensional
Method of multipliers
Cholesky Decomposition
Alternating Direction Method
Prediction Interval
Non-normality
Model
Penalization
Correlation Matrix
Sparse matrix
Closed-form Solution
Positive definite
Covariance matrix
Convergence Rate
Spectroscopy
Regression
Quantile regression
Projection

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Multitask Quantile Regression Under the Transnormal Model. / Fan, Jianqing; Xue, Lingzhou; Zou, Hui.

In: Journal of the American Statistical Association, Vol. 111, No. 516, 01.10.2016, p. 1726-1735.

Research output: Contribution to journalArticle

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