响应变量缺失下条件平均处理效应的$k$近邻核估计

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 992-1012.

• • 上一篇

响应变量缺失下条件平均处理效应的$k$近邻核估计

曾华俊^1,²,明瑞星^1,²,苏培娟^1,²,黄绍航^1,²,肖敏^1,^3,^*()

¹浙江工商大学统计数据工程技术与应用协同创新中心杭州 310018
²浙江工商大学统计与数学学院杭州 310018
³浙江工商大学经济运行态势预警与模拟推演实验室杭州 310018

收稿日期:2024-06-18 修回日期:2024-09-13 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *肖敏，Email: xiaomin@zjgsu.edu.cn
基金资助:
浙江省社会科学规划课题(22GXSZ001Z);数字+学科建设项目(SZJ2022B004);浙江省教育厅一般项目(Y202353084);浙江省登峰学科(Zhejiang Gongshang University-Statistics);Summit Advancement Disciplines of Zhejiang Province(Zhejiang Gongshang University-Statistics);浙江省省属高校基本科研业务费专项资金(XT202302)

$k$-Nearest Neighbor Kernel Estimation of Conditional Average Treatment Effect with Missing Response Variables

Zeng Huajun^1,²,Ming Ruixing^1,²,Su Peijuan^1,²,Huang Shaohang^1,²,Xiao Min^1,^3,^*()

¹Collaborative Innovation Center of Statistical Data Engineering Technology & Application, Zhejiang Gongshang University, Hangzhou 310018
²School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
³Economic Forecasting and Policy Simulation Laboratory, Zhejiang Gongshang University, Hangzhou 310018

Received:2024-06-18 Revised:2024-09-13 Online:2025-06-26 Published:2025-06-20
Supported by:
Zhejiang Provincial Philosophy and Social Sciences Planning Project(22GXSZ001Z);Digital Science and Engineering Construction Project(SZJ2022B004);Zhejiang Provincial Department of Education General Project(Y202353084);Fundamental Research Funds for the Provincial Universities of Zhejiang(XT202302)

摘要/Abstract

摘要：

基于 Neyman-Rubin 潜在结果框架, 构建 $k$ 近邻核估计量来测度响应变量随机缺失情形下的条件平均处理效应 (conditional average treatment effect, CATE), 旨在评估不同处理方式对个体的影响. 证明了 $k$ 近邻核估计量的几乎完全收敛性和渐近正态性. 数值模拟表明 $k$ 近邻核估计量的表现优良, 利用真实数据进行实证分析, 实证结果显示 $k$ 近邻核估计量具有较小的平均绝对偏差和均方根误差.

关键词: 条件平均处理效应, 随机缺失, $k$ 近邻核估计量, 渐近正态性

Abstract:

Under the Neyman-Rubin potential outcome framework, we construct a $k$-nearest neighbor kernel estimator to measure the conditional average treatment effect in the case of random missing response variables, aiming to evaluate the impact of different treatments on individuals. The paper proves the almost complete convergence and the asymptotic normality of the estimator. The numerical simulation shows that the $k$-nearest neighbor kernel estimator performs well. The real-world data is used for empirical analysis, and the empirical results show that mean absolute error and root mean square error of the $k$-nearest neighbor kernel estimator are smaller.

Key words: conditional average treatment effect, random missing, $k$-nearest neighbor kernel estimator, asymptotic normality

中图分类号:

O212.7

曾华俊, 明瑞星, 苏培娟, 黄绍航, 肖敏. 响应变量缺失下条件平均处理效应的$k$近邻核估计[J]. 数学物理学报, 2025, 45(3): 992-1012.

Zeng Huajun, Ming Ruixing, Su Peijuan, Huang Shaohang, Xiao Min. $k$-Nearest Neighbor Kernel Estimation of Conditional Average Treatment Effect with Missing Response Variables[J]. Acta mathematica scientia,Series A, 2025, 45(3): 992-1012.

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响应变量缺失下条件平均处理效应的$k$近邻核估计

$k$-Nearest Neighbor Kernel Estimation of Conditional Average Treatment Effect with Missing Response Variables

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