Nonparametric Estimation of Continuous Treatment Effect with Measurement Error
（测量误差下连续处理效应的非参数估计）
主讲人：张政（中国人民大学统计与大数据研究院助理教授）
主持老师：（北大国发院）孙振庭
参与老师：（北大经院）王一鸣、王熙、刘蕴霆
（北大国发院）沈艳、黄卓、张俊妮
（北大新结构）胡博
时间：2022年3月11日（周五） 10:00-11:30
地点（线下）：北京大学国家发展研究院承泽园245会议室
主讲人简介：
张政，中国人民大学统计与大数据研究院担任助理教授，2015年于香港中文大学统计系获博士学位。研究方向包括因果推断、缺失数据、污染数据、半参数模型的有效估计、非参数统计推断、随机微分方程、随机分析等。在JRSS-B, JOE, Quantitative Economics, JBES, Statistica Sinica, Stochastic Processes and their Applications等统计、计量经济、概率论国际期刊上发表论文十余篇。主持国家自然科学基金青年基金，北京市自然科学基金面上项目。
摘要：
We consider estimating the average dose-response function (ADRF) nonparametrically for continuous-valued treatment. The existing literature of continuous treatment effect proposed consistent estimators only for error-free data. However, in observational studies concerned by the literature of treatment effect, the treatment data can be measured with error. There, existing techniques are not applicable and finding a proper modification is not straightforward. We identify the ADRF by a weighted conditional expectation and estimate the weights nonparametrically by maximising a local generalised empirical likelihood subject to an expanding set of conditional moment equations incorporated with the deconvolution kernels. We then construct a deconvolution kernel estimator of the weighted conditional expectation. We derive the $L_2$ and $L_\infty$ convergence rates of our weights estimator and the asymptotic bias and variance of our ADRF estimator. We also provide the asymptotic linear expansion of our ADRF estimator in both the ordinary smooth and the supersmooth error cases, which can help conduct statistical inference. We provide a data-driven method to select our smoothing parameters based on the simulation-extrapolation (SIMEX) idea and propose a new extrapolation procedure to stabilise the computation. Monte-Carlo simulations show a satisfactory finite-sample performance of our method, and a real data study illustrates its practical value.
