非正则性下的交叉拟合：正态性与基于局部性的推断
Cross-Fitting Under Nonregularity: Normality and Inference via Locality
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- Stanford University（斯坦福大学）
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中文总结 AI 辅助
针对交叉拟合在非正则性下置信区间覆盖不足的问题，提出基于局部性条件的中心极限定理及调整交叉折相关性的置信区间，并通过模拟验证其近似名义覆盖率。
中文摘要 AI 辅助
交叉拟合在许多应用研究中是常规做法。尽管忽略交叉折间依赖性的传统置信区间在若干设定下具有渐近有效性，但在许多具有共同非正则性形式的应用中，它们会覆盖不足：从经典的交叉验证问题（检验拟合模型是否优于另一模型），到利用机器学习检验异质性处理效应，再到估计可能非唯一的最优治疗策略的价值。利用一个新的局部性条件，我证明了一大类交叉拟合估计量尽管存在非正则性，仍满足中心极限定理，但其渐近方差必须针对交叉折相关性进行调整。然后，我提出了一种估计这种相关性的方法，并构建了能达到渐近名义覆盖率的新的置信区间。最后，我通过随机森林和神经网络的模拟研究表明，所提出的置信区间能达到近似名义覆盖率。
英文摘要
Cross-fitting is routine in much of applied research. While conventional confidence intervals that ignore cross-fold dependence are asymptotically valid in several settings, they undercover in many applications that share a common form of nonregularity: from the classic cross-validation problem of testing whether a fitted model outperforms another, to testing for heterogeneous treatment effects with machine learning, to estimating the value of a potentially non-unique optimal treatment regime. Exploiting a new locality condition, I show that a large class of cross-fitting estimators still satisfies a central limit theorem despite the nonregularity, but with an asymptotic variance that must be adjusted for the cross-fold correlation. Then, I propose a method for estimating this correlation and construct new confidence intervals that attain asymptotically nominal coverage. Finally, I show that the proposed confidence intervals attain approximately nominal coverage in a simulation study with random forests and neural networks.
