Semiparametric counterfactual density estimation
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半参数反事实密度估计
- 研究问题
- 如何估计完整反事实密度及其泛函，以密度近似和反事实密度之间的距离刻画平均因果效应之外的分布差异？
- 方法与思路
- 作者研究广义距离下的有限维密度投影与密度间距离，推导非参数效率界，并提出双重稳健风格的估计及模型选择方法。
- 材料陈述的贡献
- 摘要称建立密度目标与特定反事实函数均值的联系，在条件满足时达到最优效率，并用 HIV 治疗数据展示密度效应。
- 阅读关注点
- 应核对反事实分布的识别条件、距离的光滑性要求、辅助估计收敛率，以及效率结论和模型聚合结果各自适用的范围。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或获期刊接收；摘要未列出识别与效率条件，治疗异质性结论仍需全文核对。
原文摘要
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. The first is a density approximation, defined by a projection onto a finite-dimensional model using a generalized distance metric, which includes f-divergences as well as $L_p$ norms. The second is the distance between counterfactual densities, which can be used as a more nuanced effect measure than the mean difference, and as a tool for model selection. We study nonparametric efficiency bounds for these targets, giving results for smooth but otherwise generic models and distances. Importantly, we show how these bounds connect to means of particular non-trivial functions of counterfactuals, linking the problems of density and mean estimation. We go on to propose doubly robust-style estimators for the density approximations and distances, and study their rates of convergence, showing 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 throughout we highlight what happens for particular choices, such as $L_2$ projections on linear models, and KL projections on exponential families. Finally we illustrate 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 results suggest combination therapy may have increased CD4 count most for high-risk patients. Our methods are implemented in the freely available R package npcausal on GitHub.