论文标题
最小值的非均质治疗效果的最佳非参数估计
Minimax Optimal Nonparametric Estimation of Heterogeneous Treatment Effects
论文作者
论文摘要
因果推断的一个核心目的是检测和估计给定治疗或干预对结果变量的治疗效果，在这种情况下，在诸如个性化医学之类的实际实用应用中，称为异质治疗效果（HTE）的成员越来越受欢迎。在本文中，我们将HTE建模为两个低光滑基线函数之间的平滑非参数差，并确定非参数HTE估计的紧密统计限制是协变量几何形状的函数。尤其是，一个两个阶段的基于邻居的估算值丢弃匹配质量差的观测值接近最佳。我们还建立了对密度比的紧密依赖性，而没有通常的假设，即协变密度远离零，在这里，关键步骤是采用新型的最大不平等现象，这可能具有独立的利益。
A central goal of causal inference is to detect and estimate the treatment effects of a given treatment or intervention on an outcome variable of interest, where a member known as the heterogeneous treatment effect (HTE) is of growing popularity in recent practical applications such as the personalized medicine. In this paper, we model the HTE as a smooth nonparametric difference between two less smooth baseline functions, and determine the tight statistical limits of the nonparametric HTE estimation as a function of the covariate geometry. In particular, a two-stage nearest-neighbor-based estimator throwing away observations with poor matching quality is near minimax optimal. We also establish the tight dependence on the density ratio without the usual assumption that the covariate densities are bounded away from zero, where a key step is to employ a novel maximal inequality which could be of independent interest.
