Nonparametric estimation of the continuous treatment effect with measurement error

• 成果类型: Article
• 署名作者: Huang, Wei; Zhang, Zheng
• 署名单位: University of Melbourne; Renmin University of China; Renmin University of China
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad013
• 发表日期: 2023
• 页码: 474-496
• 关键词: Asymptotic Normality; efficient estimation; DENSITY-ESTIMATION; propensity score; simulation-extrapolation; generalized-method; deconvolution; regression; moments; models

摘要

We identify the average dose-response function (ADRF) for a continuously valued error-contaminated treatment by a weighted conditional expectation. We then estimate the weights nonparametrically by maximising a local generalised empirical likelihood subject to an expanding set of conditional moment equations incorporated into the deconvolution kernels. Thereafter, we construct a deconvolution kernel estimator of ADRF. We derive the asymptotic bias and variance of our ADRF estimator and provide its asymptotic linear expansion, which helps conduct statistical inference. To select our smoothing parameters, we adopt the simulation-extrapolation method and propose a new extrapolation procedure to stabilise the computation. Monte Carlo simulations and a real data study illustrate our method's practical performance.