本刊英文版Vol.38(2022),No.6论文摘要

Abstracts of Acta Mathematica Sinica, English Series, Nos.6, Vol.38(2022)

Pointwise Robust Error Density Estimation in Ultrahigh Dimensional Sparse Linear Model Feng ZOU Heng Jian CUI Abstract This paper focuses on error density estimation in ultrahigh dimensional sparse linear model,where the error t erm may have a heavy-tai led distribution.First,an improved two-stage refitted cross-validation 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 met hod 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.