A smoothing iterative method for quantile regression with nonconvex ℓp penalty

Zhang, Lianjun, Kong, LingChen, Li, Yan and Zhou, Shenglong (2017) A smoothing iterative method for quantile regression with nonconvex ℓp penalty. Journal of Industrial and Management Optimization, 13 (1), 93-112. (doi:10.3934/jimo.2016006).

Record type: Article

Abstract

The high-dimensional linear regression model has attracted much attention in areas like information technology, biology, chemometrics, economics, finance and other scientific fields. In this paper, we use smoothing techniques to deal with high-dimensional sparse models via quantile regression with the nonconvex ℓp penalty (0<p<1). We introduce two kinds of smoothing functions and give the estimation of approximation by our different smoothing functions. By smoothing the quantile function, we derive two types of lower bounds for any local solution of the smoothing quantile regression with the nonconvex ℓp penalty. Then with the help of ℓ1 regularization, we propose a smoothing iterative method for the smoothing quantile regression with the weighted ℓ1 penalty and establish its global convergence, whose efficient performance is illustrated by the numerical experiments.

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