Semiparametric Counterfactual Density Estimation
Semiparametric Counterfactual Density Estimation
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DOI：
10.1093/biomet/asad017
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发表时间：
2021-02
期刊：
影响因子：
2.7
通讯作者：
Edward H. Kennedy;Sivaraman Balakrishnan;L. Wasserman
中科院分区：
文献类型：
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作者：
Edward H. Kennedy;Sivaraman Balakrishnan;L. Wasserman
因果效应通常以平均值为特征，这可能会对潜在的反事实分布产生不完整的影响。在这里，我们考虑估计整个反事实密度及其通用泛函。我们专注于两种目标参数：密度近似和反事实密度之间的距离。我们研究非参数效率的界限，光滑，但其他通用的模型和距离的结果。重要的是，我们展示了这些界限如何连接到反事实的特定非平凡函数的手段，连接密度和均值估计的问题。我们提出了双稳健型估计，并研究了它们的收敛速度，表明它们在大型非参数模型中是最优有效的。当可能有许多模型可用且感兴趣时，我们还给出了模型选择和聚合的类似方法。我们的结果都适用于通用模型和距离，但我们强调了线性模型上的L2投影和指数族上的KL投影的结果。最后，我们通过估计HIV患者的CD4计数密度来说明我们的方法，这些患者都接受了联合治疗与单用齐多夫定治疗，以及密度效应。我们的方法在GitHub上的R包npcausal中实现。
Causal effects are often characterized with averages, which can give an incomplete picture of the underlying counterfactual distributions. Here we consider estimating the entire counterfactual density and generic functionals thereof. We focus on two kinds of target parameters: density approximations and the distance between counterfactual densities. We study nonparametric efficiency bounds, giving results for smooth but otherwise generic models and distances. Importantly, we show how these bounds connect to means of particular nontrivial functions of counterfactuals, linking the problems of density and mean estimation. We propose doubly robust-style estimators, and study their rates of convergence, showing that they can be optimally efficient in large nonparametric models. We also give analogous methods for model selection and aggregation, when many models may be available and of interest. Our results all hold for generic models and distances, but we highlight results for L2 projections on linear models and KL projections on exponential families. Finally, we illustrate our method by estimating the density of CD4 count among patients with HIV, had all been treated with combination therapy versus zidovudine alone, as well as a density effect. Our methods are implemented in the R package npcausal on GitHub.