论文标题

有条件期望功能比率的正交系列估计

Orthogonal Series Estimation for the Ratio of Conditional Expectation Functions

论文作者

Shinoda, Kazuhiko, Hoshino, Takahiro

论文摘要

在数据科学的各个领域,研究人员通常对估计条件期望功能的比率(CEFR)感兴趣。特别是在因果推理问题上,有时自然要考虑基于比率的治疗效应,例如优势比和危害比,甚至基于差异的治疗效应在某些经验上相关的环境中被确定为CEFR。本章开发了对CEFR估计和推断的一般框架,该框架允许将灵活的机器学习用于无限维滋扰参数。在框架的第一阶段,使用偏见的机器学习技术构建正交信号,以减轻正则化偏差对目标估计的负面影响的负面影响。然后将信号与针对CEFR量身定制的新型系列估计器结合使用。我们为CEFR的估计和推断(包括高斯自举的有效性)得出了渐近和均匀的渐近结果,并提供了低水平的足够条件,以将建议的框架应用于某些特定示例。我们证明了通过数值模拟在拟议的框架下构建的系列估计器的有限样本性能。最后,我们应用了提出的方法来估计401(k)计划对家庭资产的因果影响。

In various fields of data science, researchers are often interested in estimating the ratio of conditional expectation functions (CEFR). Specifically in causal inference problems, it is sometimes natural to consider ratio-based treatment effects, such as odds ratios and hazard ratios, and even difference-based treatment effects are identified as CEFR in some empirically relevant settings. This chapter develops the general framework for estimation and inference on CEFR, which allows the use of flexible machine learning for infinite-dimensional nuisance parameters. In the first stage of the framework, the orthogonal signals are constructed using debiased machine learning techniques to mitigate the negative impacts of the regularization bias in the nuisance estimates on the target estimates. The signals are then combined with a novel series estimator tailored for CEFR. We derive the pointwise and uniform asymptotic results for estimation and inference on CEFR, including the validity of the Gaussian bootstrap, and provide low-level sufficient conditions to apply the proposed framework to some specific examples. We demonstrate the finite-sample performance of the series estimator constructed under the proposed framework by numerical simulations. Finally, we apply the proposed method to estimate the causal effect of the 401(k) program on household assets.

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