Nonparametric estimation of the continuous treatment effect with measurement error
针对连续型处理变量存在测量误差的问题，通过加权条件期望识别平均剂量反应函数，并利用局部广义经验似然和去卷积核方法进行非参数估计，为实证研究者提供了一种新的统计推断工具。
Abstract 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.