Robust Error Density Estimation in Ultrahigh Dimensional Sparse Linear Model  

作　　者：Feng ZOU Heng Jian CUI 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第6期963-984,共22页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11971324);the State Key Program of National Natural Science Foundation of China(Grant No.12031016)。

摘　　要：This paper focuses on error density estimation in ultrahigh dimensional sparse linear model,where the error term may have a heavy-tailed distribution.First,an improved two-stage refitted crossvalidation method combined with some robust variable screening procedures such as RRCS and variable selection methods such as LAD-SCAD is used to obtain the submodel,and then the residual-based kernel density method is applied to estimate the error density through LAD regression.Under given conditions,the large sample properties of the estimator are also established.Especially,we explicitly give the relationship between the sparsity and the convergence rate of the kernel density estimator.The simulation results show that the proposed error density estimator has a good performance.A real data example is presented to illustrate our methods.

关 键 词：Ultrahigh dimensional sparse linear model robust density estimation refitted crossvalidation method asymptotic properties 

分 类 号：O212.1[理学—概率论与数理统计]