Multitask Quantile Regression under the Transnormal Model.

ABSTRACT: We consider estimating multi-task 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 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 nonn

SUBMITTER: Fan J 

PROVIDER: S-EPMC5662245 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature