维数发散乘积回归模型的M估计  

The M-Estimation for Multiplicative Regression Models with a Diverging Number of Covariates

作　　者：范瑞雅 张曙光[2] 吴耀华[2] FAN Ruiya;ZHANG Shuguang;WU Yaohua(School of Mathematics and Physics,Southwest University of Science and Technology,Mianyang,621010,China;Department of Statistics and Finance,University of Science and Technology of China,Hefei,230026,China)

机构地区：[1]西南科技大学数理学院,绵阳621010 [2]中国科学技术大学统计与金融系,合肥230026

出　　处：《应用概率统计》2024年第1期33-49,共17页Chinese Journal of Applied Probability and Statistics

基　　金：西南科技大学博士基金项目(批准号:22zx7105);安徽省自然科学基金项目(批准号:202006f01050060)资助。

摘　　要：针对乘积回归模型,本文提出了非凹惩罚最小乘积相对误差的M估计(简称为惩罚MLPRE),该方法可有效处理高维样本量及参数维数随样本量增大而增大的稀疏乘积回归模型.基于一些正则条件,本文得到惩罚M-LPRE参数估计的相合性和渐近正态性等理论性质,通过数值模拟和实例分析,验证了惩罚M-LPRE准则的有效性.In this article,we propose a nonconcave penalized M-estimation of least product relative error(penalized M-LPRE)method for multiplicative regression models whose dimension of parameters is sparse and can increase with the sample size.Under some mild conditions,consistency and asymptotic normality of the penalized M-LPRE estimator are established.Numerical simulations and a real data analysis on the body fat are carried out to assess the performance of the proposed method.

关 键 词：惩罚LPRE M估计 乘积回归模型 

分 类 号：O212.1[理学—概率论与数理统计]