Randomization inference provides exact finite sample tests of sharp null hypotheses which fully specify the distribution of outcomes under counterfactual realizations of treatment, but the sharp null is often considered restrictive as it rules out unspecified heterogeneity in treatment response. However, a growing literature shows that tests based upon permutations of regressors using pivotal statistics can remain asymptotically valid when the assumption regarding the permutation invariance of the data generating process used to motivate them is actually false. For experiments where potential outcomes involve the permutation of regressors, these results show that permutation-based randomization inference, while providing exact tests of sharp nulls, can also have the same asymptotic validity as conventional tests of average treatment effects with unspecified heterogeneity and other forms of specification error in treatment response. This paper extends this work to the consideration of interactions between treatment variables and covariates, a common feature of published regressions, as well as issues in the construction of confidence intervals and testing of subsets of treatment effects.

中文翻译：

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用于参数 OLS 回归的渐近鲁棒基于排列的随机化置信区间

随机化推理提供了尖锐零假设的精确有限样本检验，这些假设完全指定了治疗反事实实现下结果的分布，但尖锐零通常被认为是限制性的，因为它排除了治疗反应中未指定的异质性。然而，越来越多的文献表明，当用于激励测试的数据生成过程的排列不变性的假设实际上是错误的时，基于使用关键统计数据的回归量排列的测试可以保持渐近有效。对于潜在结果涉及回归变量排列的实验，这些结果表明，基于排列的随机化推理在提供尖锐零点的精确测试的同时，也可以与具有未指定异质性和其他形式的平均治疗效果的传统测试具有相同的渐近有效性。治疗反应中的规范错误。本文将这项工作扩展到考虑治疗变量和协变量之间的相互作用（已发表的回归的一个共同特征），以及构建置信区间和测试治疗效果子集的问题。