Causal Inference on Quantile Dose-response Functions via Local ReLU Least Squares Weighting
报告人: 张政(中国人民大学)
时间:2024-04-25 15:10-17:00
地点:光华2号楼217
Abstract:
This paper proposes a novel local ReLU network least squares weighting method to estimate quantile dose-response functions in observational studies. Unlike the conventional inverse propensity weighting (IPW) method, we estimate the weighting function involved in the treatment effect estimator directly through local ReLU least squares optimization. The proposed method takes advantage of ReLU networks applied for the baseline covariates with increasing dimension to alleviate the dimensionality problem while retaining flexibility and local kernel smoothing for the continuous treatment to precisely estimate the quantile dose-response function and prepare for statistical inference. Our method enjoys computational convenience and scalability. It also improves robustness and numerical stability compared to the conventional IPW method. For the ReLU network approximation, we introduce a mixed fractional Sobolev class and show that the two-layer ReLU networks can break the `curse of dimensionality' when the weighting function belongs to this function class. We also establish the convergence rate for the ReLU network estimator and the asymptotic normality of the proposed estimator for the quantile dose-response function. We further propose a multiplier bootstrap method to construct confidence bands for quantile dose-response functions. The finite sample performance of our proposed method is illustrated through simulations and a real data application.
About the Speaker:
张政,中国人民大学统计与大数据研究院长聘副教授。2015年于香港中文大学统计系获博士学位。研究方向为因果推断、处理效应模型。迄今在JRSS-B, Quantitative Economics, JOE, JBES等统计与计量经济期刊发表论文十余篇。主持国家自然科学基金两项、北京市自然科学基金一项。
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