Error-Function-Based Penalized Quantile Regression in the Linear Mixed Model - Zelin Hang; Xiuli He (Applied Sciences)
We study a novel Doubly penalized ERror Function regularized Quantile Regression (DERF-QR) in this paper. This is a method of variable selection by ERror Function (ERF) regularization in the linear effects model. We introduce a two-stage iterative algorithm combining the iterative reweighted <semantics>L1</semantics> approach and the alternating direction method of multipliers (ADMM) to estimate the model parameters. Numerical simulations show that by using this method we remove redundant variables effectively and obtain accurate coefficient estimations. Our method outperforms two existing penalized quantile regression methods in various error conditions by comparison. Finally, we apply the methodology in a financial dataset and showcase its practicality.