Prof. Yuwen Gu Department of Statistics University of Connecticut

Sparse Penalized Quantile Regression: Method, Theory, and Algorithm

Sparse penalized quantile regression is a useful tool for variable selection, robust estimation, and heteroscedasticity detection in high-dimensional data analysis. We discuss the variable selection and estimation properties of the lasso and folded concave penalized quantile regression via non-asymptotic arguments. We also consider consistent parameter tuning therein. The computational issue of the sparse penalized quantile regression has not yet been fully resolved in the literature, due to non-smoothness of the quantile regression loss function. We introduce fast alternating direction method of multipliers (ADMM) algorithms for computing the sparse penalized quantile regression. Numerical examples demonstrate the competitive performance of our algorithm: it significantly outperforms several other fast solvers for high-dimensional penalized quantile regression.