Abstract 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.

中文翻译：

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高维模型中治疗效果的无偏推断

摘要 本文涉及当线性或部分线性模型中存在大量协变量时，对治疗效果的统计推断中的潜在偏差。虽然欠拟合模型中的估计偏差是众所周知的，但我们解决了由过拟合模型引起的鲜为人知的偏差。可以通过以统计效率为代价的数据拆分来消除过拟合偏差，并且我们表明可以追求对随机数据拆分的平滑以减轻效率损失。我们还讨论了一些现有的去偏推理方法，并提供了对其内在偏差 - 方差权衡的见解，从而改进了偏差控制。在适当的条件下，我们表明，建议的治疗效果估计量是渐近正态的，并且可以很好地估计它们的方差。我们从理论和经验上讨论了各种方法的优缺点，并表明所提出的方法是选择后推理中有价值的选择。本文的补充材料可在线获取。