Model averaging with causal effects for partially linear models

Xiaowei Zhang; Junliang Li; Xiaowei Zhang; Junliang Li

doi:10.3934/math.2024794

AIMS Mathematics

2024, Volume 9, Issue 6: 16392-16421. doi: 10.3934/math.2024794

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Theory article

Model averaging with causal effects for partially linear models

Xiaowei Zhang ^{1
,
,},
Junliang Li ²

1.
Department of Statistics and Data Science, School of Economics, Jinan University, Guangzhou, 510632, China
2.
The second middle school of yuncheng county, Heze city of Shandong Province, 274700, China

Received: 04 January 2024 Revised: 30 April 2024 Accepted: 06 May 2024 Published: 09 May 2024
MSC : 62F40, 62G20, 62G99

Treatment effects with heterogeneity and heteroskedasticity are widely studied and applied in many fields, such as statistics and econometrics. The conditional average treatment effect provides an excellent measure of the heterogeneous treatment effect. In this paper, we propose a model averaging estimation for the conditional average treatment effect with partially linear models based on the jackknife-type criterion under heteroscedastic error. Within this context, we provide theoretical justification for our model averaging approach, and we establish asymptotic optimality and weight convergence properties for our model under certain conditions. The performance of our proposed estimator is compared with that of classical estimators by using a Monte Carlo study and empirical analysis.
- model averaging,
- causal inference,
- partially linear models,
- conditional average treatment effect,
- Jackknife-type criterion
Citation: Xiaowei Zhang, Junliang Li. Model averaging with causal effects for partially linear models[J]. AIMS Mathematics, 2024, 9(6): 16392-16421. doi: 10.3934/math.2024794

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Abstract

Treatment effects with heterogeneity and heteroskedasticity are widely studied and applied in many fields, such as statistics and econometrics. The conditional average treatment effect provides an excellent measure of the heterogeneous treatment effect. In this paper, we propose a model averaging estimation for the conditional average treatment effect with partially linear models based on the jackknife-type criterion under heteroscedastic error. Within this context, we provide theoretical justification for our model averaging approach, and we establish asymptotic optimality and weight convergence properties for our model under certain conditions. The performance of our proposed estimator is compared with that of classical estimators by using a Monte Carlo study and empirical analysis.

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