Randomization Tests for Weak Null Hypotheses in Randomized Experiments
随机实验中弱零假设的随机化检验AI 解读 ↓
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随机实验中弱零假设的随机化检验
- 研究问题
- 当零假设只限制平均处理效应而不能恢复所有缺失潜在结果时，如何实施 Fisher 随机化检验，并在效应异质性下控制第一类错误？
- 方法与思路
- 作者用与弱零假设相容的尖锐零假设插补缺失潜在结果，结合学生化统计量构造检验，并扩展至一般析因、分层和整群实验。
- 材料陈述的贡献
- 摘要称，检验在用于插补的尖锐零假设下有限样本精确，在目标弱零假设下保守控制大样本第一类错误，并允许处理效应异质性。
- 阅读关注点
- 应核对相容尖锐零假设的构造、学生化方差估计和随机化方式，尤其区分尖锐零假设下的有限样本性质与弱零假设下的渐近性质。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要，具体渐近条件未说明；不能将尖锐零假设下的有限样本精确性延伸为弱零假设下同样精确。
原文摘要
The Fisher randomization test (FRT) is appropriate for any test statistic, under a sharp null hypothesis that can recover all missing potential outcomes. However, it is often sought after to test a weak null hypothesis that the treatment does not affect the units on average. To use the FRT for a weak null hypothesis, we must address two issues. First, we need to impute the missing potential outcomes although the weak null hypothesis cannot determine all of them. Second, we need to choose a proper test statistic. For a general weak null hypothesis, we propose an approach to imputing missing potential outcomes under a compatible sharp null hypothesis. Building on this imputation scheme, we advocate a studentized statistic. The resulting FRT has multiple desirable features. First, it is model-free. Second, it is finite-sample exact under the sharp null hypothesis that we use to impute the potential outcomes. Third, it conservatively controls large-sample Type I error under the weak null hypothesis of interest. Therefore, our FRT is agnostic to the treatment effect heterogeneity. We establish a unified theory for general factorial experiments and extend it to stratified and clustered experiments. Supplementary materials for this article are available online.