Huang Ming-Yueh, Chan Kwun Chuen Gary
Institute of Statistical Science, Academia Sinica, Taiwan.
Department of Biostatistics, University of Washington, U.S.A.
J Multivar Anal. 2018 Nov;168:48-62. doi: 10.1016/j.jmva.2018.07.005. Epub 2018 Jul 10.
The estimation of continuous treatment effect functions using observational data often requires parametric specification of the effect curves, the conditional distributions of outcomes and treatment assignments given multi-dimensional covariates. While nonparametric extensions are possible, they typically suffer from the curse of dimensionality. Dimension reduction is often inevitable and we propose a sufficient dimension reduction framework to balance parsimony and flexibility. The joint central subspace can be estimated at a -rate without fixing its dimension in advance, and the treatment effect function is estimated by averaging local estimates of a reduced dimension. Asymptotic properties are studied. Unlike binary treatments, continuous treatments require multiple smoothing parameters of different asymptotic orders to borrow different facets of information, and their joint estimation is proposed by a non-standard version of the infinitesimal jackknife.
使用观测数据估计连续治疗效应函数通常需要对效应曲线、给定多维协变量时结果和治疗分配的条件分布进行参数化设定。虽然非参数扩展是可行的，但它们通常会受到维度诅咒的影响。降维往往不可避免，我们提出了一个充分降维框架来平衡简约性和灵活性。联合中心子空间可以以 - 速率进行估计，而无需事先固定其维度，并且通过对降维后的局部估计进行平均来估计治疗效应函数。我们研究了渐近性质。与二元治疗不同，连续治疗需要多个具有不同渐近阶的平滑参数来借用不同方面的信息，并且通过一种非标准版本的无穷小刀切法来进行它们的联合估计。
