纵向数据下变系数模型的一种稳健同质寻踪算法  

A robust homogeneity pursuit algorithm for varying coefficient models with longitudinal data

作　　者：汤恒 郑智 张伟平[1] TANG Heng;ZHENG Zhi;ZHANG Weiping(Department of Statistics and Finance,School of Management,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学管理学院统计与金融系,安徽合肥230026

出　　处：《中国科学技术大学学报》2021年第12期857-867,共11页JUSTC

基　　金：supported by the National Natural Science Foundation of China(Nos.12171450,71771203).

摘　　要：探讨了变系数模型中参系数函数的同质性,其中同一个子群中的个体的系数函数是相同的.在重复观测的条件下,我们用B样条来拟合变系数模型的系数函数,同时用变点检测的方法来进行子群识别.为了解释可能的异常值或重尾分布,我们在M估计的框架下拟合系数函数,在本文中以绝对值(LAD)损失为例.模拟数据表明,当模拟数据集存在异常值或参数函数为重尾分布时,我们的估计方法优于常用的最小二乘(LS)估计.This article explores the homogeneity of coefficient functions in varying coefficient models where individuals can be classified into different subgroups for each covariate where its varying coefficients are homogeneous in the same subgroup.With repeated measurements,we use B-spline function approximations and the change point detection algorithm to identify the homogeneity.To account for the potential outliers or heavy-tailedness of the observed distribution,we propose to estimate the coefficient functions under the framework of M-estimation,and use least absolute deviation(LAD)loss as an example.Numerical results show that our estimators outperform the commonly used least squares(LS)estimators when existing outliers and heavy-tailedness of observed distribution.

关 键 词：变系数模型 M估计 B样条 变点检测 同质寻踪 

分 类 号：O212.1[理学—概率论与数理统计]