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 n 1/2-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.

中文翻译：

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用于估计连续治疗效果函数的联合充分降维

使用观察数据估计连续治疗效果函数通常需要对效果曲线、结果的条件分布和给定多维协变量的治疗分配进行参数说明。虽然非参数扩展是可能的，但它们通常会受到维度灾难的影响。降维通常是不可避免的，我们提出了一个足够的降维框架来平衡简约性和灵活性。联合中心子空间可以在不预先固定其维度的情况下以 1/2 的比率进行估计，并且通过对减少的维度的局部估计进行平均来估计治疗效果函数。研究了渐近特性。与二元处理不同，