Semiparametric expectile regression for high-dimensional heavy-tailed and heterogeneous data  

作　　者：ZHAO Jun YAN Guan-ao ZHANG Yi 

机构地区：[1]Institute of Digital Finance,Hangzhou City University,Hangzhou 310015,China [2]Department of Statistics,Hangzhou City University,Hangzhou 310015,China [3]Department of Statistics,University of California,Los Angeles,CA 90095,USA [4]School of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2025年第1期53-77,共25页高校应用数学学报(英文版)(B辑)

基　　金：Supported by the Hangzhou Joint Fund of the Zhejiang Provincial Natural Science Foundation of Chi-na(LHZY24A010002);the MOE Project of Humanities and Social Sciences(21YJCZH235).

摘　　要：High-dimensional heterogeneous data have acquired increasing attention and discussion in the past decade.In the context of heterogeneity,semiparametric regression emerges as a popular method to model this type of data in statistics.In this paper,we leverage the benefits of expectile regression for computational efficiency and analytical robustness in heterogeneity,and propose a regularized partially linear additive expectile regression model with a nonconvex penalty,such as SCAD or MCP,for high-dimensional heterogeneous data.We focus on a more realistic scenario where the regression error exhibits a heavy-tailed distribution with only finite moments.This scenario challenges the classical sub-gaussian distribution assumption and is more prevalent in practical applications.Under certain regular conditions,we demonstrate that with probability tending to one,the oracle estimator is one of the local minima of the induced optimization problem.Our theoretical analysis suggests that the dimensionality of linear covariates that our estimation procedure can handle is fundamentally limited by the moment condition of the regression error.Computationally,given the nonconvex and nonsmooth nature of the induced optimization problem,we have developed a two-step algorithm.Finally,our method’s effectiveness is demonstrated through its high estimation accuracy and effective model selection,as evidenced by Monte Carlo simulation studies and a real-data application.Furthermore,by taking various expectile weights,our method effectively detects heterogeneity and explores the complete conditional distribution of the response variable,underscoring its utility in analyzing high-dimensional heterogeneous data.

关 键 词：expectile regression HETEROGENEITY heavy tail partially linear additive model 

分 类 号：O22[理学—运筹学与控制论]