响应变量缺失下条件平均处理效应的$k$近邻核估计

Abstract

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

CLC Number:

O212.7

Huajun Zeng, Ruixing Ming, Peijuan Su, Shaohang Huang, Min Xiao. $k$ -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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References 30

[1]	Rosenbaum P R, Rubin D B. The central role of the propensity score in observational studies for causal effects. Biometrika, 1983, 70(1): 41-55
[2]	Rosenbaum P R, Rubin D B. Constructing a control group using multivariate matched sampling models that incorporate the propensity score. Amer Statist, 1985, 39(1): 33-38
[3]	Caron A, Baio G, Manolopoulou I. Estimating individual treatment effects using non-parametric regression models: A review. J Roy Statist Soc Ser A, 2022, 185(3): 1115-1149
[4]	Yao L Y, Chu Z X, Li S, et al. A survey on causal inference. ACM Transactions on Knowledge Discovery from Data, 2021, 15(5): 1-46
[5]	Sarraju A, Ward A, Li J, et al. Personalizing cholesterol treatment recommendations for primary cardiovascular disease prevention. Sci Rep, 2022, 12(1): Article 23
[6]	Sorace M. The ties that unbind: Intergovernmental decision rules and the policy-opinion link. J Eur Public Policy, 2023, 30(8): 1609-1632
[7]	Zhang Z W, Liu W, Zhang B, et al. Causal inference with missing exposure information: Methods and applications to an obstetric study. Stat Methods Med Res, 2016, 25(5): 2053-2066 pmid: 24318273
[8]	Abrevaya J, Hsu Y C, Lieli R P. Estimating conditional average treatment effects. J Bus Econom Statist, 2015, 33(4): 485-505
[9]	Li L, Zhou N W, Zhu L X. Outcome regression-based estimation of conditional average treatment effect. Ann Inst Statist Math, 2022, 74(5): 987-1041
[10]	Kudraszow N L, Vieu P. Uniform consistency of kNN regressors for functional variables. Statist Probab Lett, 2013, 83(8): 1863-1870
[11]	Ling N X, Meng S Y, Vieu P. Uniform consistency rate of kNN regression estimation for functional time series data. J Nonparametr Stat, 2019, 31(2): 451-468
[12]	Friedman J H. Greedy function approximation: A gradient boosting machine. Ann Statist, 2001, 29: 1189-1232
[13]	Chen T Q, Guestrin C. Xgboost: A scalable tree boosting system//Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016, 785-794
[14]	Breiman L. Random forests. Mach Learn, 2001, 45(1): 5-32
[15]	Wager S, Athey S. Estimation and inference of heterogeneous treatment effects using random forests. J Amer Statist Assoc, 2018, 113(523): 1228-1242
[16]	Athey S, Wager S. Estimating treatment effects with causal forests: An application. Observ Stud, 2019, 5(2): 37-51
[17]	Little R J, D'agostino R, Cohen M L, et al. The prevention and treatment of missing data in clinical trials. New Engl J Med, 2012, 367(14): 1355-1360
[18]	Ocampo A, Schmidli H, Quarg P, et al. Identifying treatment effects using trimmed means when data are missing not at random. Pharm Stat, 2021, 20(6): 1265-1277 doi: 10.1002/pst.2147 pmid: 34169641
[19]	Kuzmanovic M, Hatt T, Feuerriegel S. Estimating conditional average treatment effects with missing treatment information//Proceedings of the 26th International Conference on Artificial Intelligence and Statistics. Valencia: PMLR, 2023, 746-766
[20]	Stensrud M J, Robins J M, Sarvet A, et al. Conditional separable effects. J Amer Statist Assoc, 2023, 118(544): 2671-2683
[21]	Zhao A Q, Peng D. To adjust or not to adjust? Estimating the average treatment effect in randomized experiments with missing covariates. J Amer Statist Assoc, 2024, 119(545): 450-460
[22]	苗旺, 刘春辰, 耿直. 因果推断的统计方法. 中国科学: 数学, 2018, 48(12): 1753-1778
	Miao W, Liu C C, Geng Z. Statistical approaches for causal inference (in Chinese). Sci Sin Math, 2018, 48(12): 1753-1778 (in Chinese).
[23]	Greenland S, Pearl J, Robins J M. Confounding and collapsibility in causal inference. Statist Sci, 1999, 14(1): 29-46
[24]	Geng Z, Guo J H, Fung W K. Criteria for confounders in epidemiological studies. J R Stat Soc Ser B Stat Methodol, 2002, 64(1): 3-15
[25]	Han P S. Multiply robust estimation in regression analysis with missing data. J Amer Statist Assoc, 2014, 109(507): 1159-1173
[26]	Ferraty F, Laksaci A, Tadj A, et al. Rate of uniform consistency for nonparametric estimates with functional variables. J Statist Plann Inference, 2010, 140(2): 335-352
[27]	Hill J L. Bayesian nonparametric modeling for causal inference. J Comput Graph Statist, 2011, 20(1): 217-240
[28]	Burba F, Ferraty F, Vieu P. $k$ -Nearest neighbour method in functional nonparametric regression. J Nonparametr Stat, 2009, 21(4): 453-469
[29]	Ezzahrioui M, Ould-Saïd E. Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data. J Nonparametr Stat, 2008, 20(1): 3-18
[30]	黄绍航. 随机缺失下条件平均处理效果的 $k$ 近邻核估计. 杭州: 浙江工商大学, 2022
	Huang S H. $K$ -nearest Neighbor Kernel Estimation of Conditional Average Treatment Effect Under Random Missing Data. Hangzhou: Zhejiang Gongshang University, 2022

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

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

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