超高维线性回归模型基于M-估计方法的变量选择和参数估计  

Variable Selection and Parameter Estimation with M-Estimation Method for Ultra-high Dimensional Linear Model

作　　者：朱艳玲[1] 汪凯[1] 赵明涛[1] ZHU Yanling;WANG Kai;ZHAO Mingtao(School of Statistics and Applied Mathematics,Anhui University of Finance and Economics,Bengbu 233000,China)

机构地区：[1]安徽财经大学统计与应用数学学院,安徽蚌埠233000

出　　处：《应用数学》2021年第4期912-921,共10页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(71803001);Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province(gxyqZD2019031);the Social Science Foundation of China(15CTJ008)。

摘　　要：本文考虑超高维情形下线性回归模型的变量选择和参数估计问题.利用M-估计方法,将最小二乘、最小一乘、分位数回归以及Huber回归统一到一般性框架下,证明了提出的惩罚似然M-估计量具有良好的大样本性质;利用向后回归与局部线性回归相结合的方法进行变量选择和参数估计,数值模拟表现较好.在超高维情形下,我们提出的一般性方法在变量选择和参数估计方面具有较好的稳健性和有效性.In this paper, the variable selection and parameter estimation of linear regression model in ultra-high dimensional case are considered. The proposed penalty likelihood M-estimator is proved to have good large sample properties by unifying the least squares, least absolute deviation, quantile regression and Huber regression into a general framework. The variable selection and parameter estimation are performed best by combining backward regression with local linear regression in the numerical simulation. In the case of ultra-high dimension, our general method has good robustness and effectiveness in variable selection and parameter estimation.

关 键 词：超高维模型 M-估计 惩罚似然 变量选择 

分 类 号：O212.1[理学—概率论与数理统计]