A0303
Title: Sparse composite quantile regression with consistent parameter tuning
Authors: Yuwen Gu - University of Connecticut (United States) [presenting]
Hui Zou - University of Minnesota (United States)
Abstract: Composite quantile regression (CQR) provides an efficient estimation of the coefficients in linear models, regardless of the error distributions. We consider penalized CQR for both variable selection and efficient coefficient estimation in a linear model under ultrahigh dimensionality and possibly heavy-tailed error distribution. Both lasso and folded concave penalties are discussed. An $L_2$ risk bound is derived for the lasso estimator to establish its estimation consistency and the strong oracle property of the folded concave penalized CQR is shown for a feasible solution via the LLA algorithm. Information criteria for selecting the regularization parameter in the folded concave penalized CQR are proposed and shown to be selection consistent. The nonsmooth nature of the penalized CQR poses great numerical challenges for high-dimensional data. We provide a unified and effective numerical optimization algorithm for computing penalized CQR via ADMM. We demonstrate the superior efficiency of penalized CQR estimator, as compared to the penalized least squares estimator, through simulated data under various error distributions.
