This paper considers a generalized optimization framework for the estimation of general heterogeneous treatment (GHTE) effects when the covariates are exposed to classical measurement errors. The framework includes the conditional average, quantile, and asymmetric least squares causal effects of treatment as special cases. Under the unconfoundedness condition, we show that GHTE can be identified through a weighted optimization based on which we propose deconvolution kernel estimators. We derive the asymptotic bias and variance of our proposed estimators and provide their asymptotic linear expansions, which is useful for statistical inference in practice. We adopt the simulation-extrapolation method to select the smoothing parameters and propose a new extrapolation procedure to stabilize the computation. Monte Carlo simulations and real data analysis support the benefits of our estimators under measurement error.

张政，中国人民大学统计与大数据研究院长聘副教授。2011年于东南大学数学系获学士学位，2015年于香港中文大学统计系获博士学位。研究的主要方向为因果推断、处理效应模型。迄今在JRSS-B, JOE, JBES, Quantitative Economics，Stochastic Processes and their Applications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一项、北京市自然科学基金一项，参与科技部重点研发项目一项。