High-dimensional expectile regression incorporating graphical structure among predictors

Abstract

ABSTRACT With the extensive application of high-dimensional heterogeneous data in various disciplines, sparse expectile regression is increasingly favoured by people. In this paper, we make use of the graphical structure among predictors node-by-node to improve the performance of parameter estimation, model selection and prediction in sparse expectile regression. A modified alternating direction method of multipliers (ADMM) algorithm with a linearization trick is proposed to implement the proposed method numerically, and the convergence of the algorithm is proved. Simulation studies are conducted to evaluate the finite-sample performance of the proposed method. We demonstrate the practicability of the proposed approach with a dataset of the expression quantitative trait locus mapping (eQTL) experiment in Rattus norvegicus.