基于多响应回归的子群分析

doi:10.52396/JUST-2021-0053

中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (3): 216-227.DOI: 10.52396/JUST-2021-0053

基于多响应回归的子群分析

吴捷^1,2, 周佳^1,2*, 郑泽敏^1,2*

1.中国科学技术大学国际金融研究院,安徽合肥 230601;
2.中国科学技术大学管理学院,安徽合肥 230026

收稿日期:2021-03-08 修回日期:2021-03-28 出版日期:2021-03-31 发布日期:2021-11-16
通讯作者: *E-mail:tszhjia@mail.ustc.edu.cn; zhengzm@ustc.edu.cn

Subgroup analysis for multi-response regression

Wu Jie^1,2, Zhou Jia^1,2*, Zheng Zemin^1,2*

1. International Institute of Finance, University of Science and Technology of China, Hefei 230601, China;
2. School of Management, University of Science and Technology of China, Hefei 230026, China

Received:2021-03-08 Revised:2021-03-28 Online:2021-03-31 Published:2021-11-16
Contact: *E-mail: tszhjia@mail.ustc.edu.cn; zhengzm@ustc.edu.cn

摘要/Abstract

摘要： 由于研究异质效应可以消除个体差异的影响,使估计结果更加准确,因此在现代大数据应用中,正确识别异质群体中的亚群越来越受欢迎.尽管文献增长迅速,但现有的方法大多集中在异质单响应回归上,如何在多响应问题中准确识别亚组仍不清楚.本文提出了一种新的基于凹融合的异质多响应回归方法,该方法能同时估计系数矩阵并识别子群结构.此外,通过建立估计一致性,为所提出的方法提供了理论保证.数值研究证明了该方法的有效性.

关键词: 多响应回归, 子群分析, 凹惩罚, ADMM算法

Abstract: Correctly identifying the subgroups in a heterogeneous population has gained increasing popularity in modern big data applications since studying the heterogeneous effect can eliminate the impact of individual differences and make the estimation results more accurate. Despite the fast growing literature, most existing methods mainly focus on the heterogeneous univariate regression and how to precisely identify subgroups in face of multiple responses remains unclear. Here, we develop a new methodology for heterogeneous multi-response regression via a concave pairwise fusion approach, which estimates the coefficient matrix and identifies the subgroup structure jointly. Besides, we provide theoretical guarantees for the proposed methodology by establishing the estimation consistency. Our numerical studies demonstrate the effectiveness of the proposed method.

Key words: multi-response regression, subgroup analysis, concave penalties, ADMM algorithm

中图分类号:

吴捷, 周佳, 郑泽敏. 基于多响应回归的子群分析[J]. 中国科学技术大学学报, 2021, 51(3): 216-227.

WU Jie, ZHOU Jia, ZHENG Zemin. Subgroup analysis for multi-response regression[J]. Journal of University of Science and Technology of China, 2021, 51(3): 216-227.

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基于多响应回归的子群分析

Subgroup analysis for multi-response regression

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