Debiased Inference on Treatment Effect in a High Dimensional Model
Debiased Inference on Treatment Effect in a High Dimensional Model
复制标题
高维模型中治疗效果的去偏推断
DOI：
10.1080/01621459.2018.1558062
复制
发表时间：
2019
影响因子：
3.7
通讯作者：
Xu, Gongjun
中科院分区：
文献类型：
--
作者：
Wang, Jingshen;He, Xuming;Xu, Gongjun
本文关注的是当线性或部分线性模型中存在大量协变量时，在治疗效果的统计推断中的潜在偏差。虽然低拟合度模型中的估计偏差是很好理解的，但我们解决了一个不太为人所知的偏差，这是由过拟合模型引起的。过拟合偏差可以通过数据分割来消除，但代价是统计效率，我们证明了可以通过对随机数据分割进行平滑来减少效率损失。我们还讨论了一些现有的无偏推理方法，并对它们内在的偏差-方差权衡提供了见解，这导致了偏差控制的改善。在适当的条件下，我们证明了所提出的处理效应估计是渐近正态的，并且它们的方差可以很好地估计。我们从理论和实证两个方面讨论了各种方法的优缺点，并表明所提出的方法在后选择推理中是有价值的选择。这篇文章的补充材料可以在网上找到。
This article concerns the potential bias in statistical inference on treatment effects when a large number of covariates are present in a linear or partially linear model. While the estimation bias in an under-fitted model is well understood, we address a lesser-known bias that arises from an over-fitted model. The over-fitting bias can be eliminated through data splitting at the cost of statistical efficiency, and we show that smoothing over random data splits can be pursued to mitigate the efficiency loss. We also discuss some of the existing methods for debiased inference and provide insights into their intrinsic bias-variance trade-off, which leads to an improvement in bias controls. Under appropriate conditions, we show that the proposed estimators for the treatment effects are asymptotically normal and their variances can be well estimated. We discuss the pros and cons of various methods both theoretically and empirically, and show that the proposed methods are valuable options in post-selection inference. Supplementary materials for this article are available online.