Multi-Task Quantile Regression Under the Transnormal Model

• Activity Number: 208
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Jianqing Fan*+ and Lingzhou Xue and Hui Zou
• Companies: Princeton University and Penn State and University of Minnesota
• Keywords: Suprious correlations ; High-dimensional statistics ; Model selection ; hypothesis testing ; random geometry

Abstract

We consider high-dimensional multi-task quantile regression under the transnormal model. We derive a simple closed-form solution through rank-based covariance regularization. In particular, we propose the rank-based L1 penalization for estimating sparse covariance matrices, and the rank-based banded Cholesky decomposition regularization for estimating banded precision matrices.Our work combines strengths of quantile regression and rank-based covariance regularization to simultaneously deal with nonlinearity, nonnormality and high dimensionality for high-dimensional regression. Furthermore, the proposed method strikes a nice balance between robustness and efficiency, and achieves the ``oracle''-like convergence rate under the high-dimensional setting where dimension is at a nearly exponential rate to sample size. The finite-sample performance of the proposed method is also examined. The superior performance of our proposed rank-based method is demonstrated in a real application to analyze the call center arrival data.