On the Behavior of Randomization Tests without a Group Invariance Assumption
缺少群不变性假设时随机化检验的表现AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究一般假设检验的群不变性与稳健性，随机化术语本身不足以归入经济因果推断。
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缺少群不变性假设时随机化检验的表现
- 研究问题
- 当数据分布不满足构造随机化检验所需的群不变性时，检验能否仍在渐近意义上维持名义第一类错误率？
- 方法与思路
- 作者研究不变性失效后的渐近水平，分别分析单样本均值或中位数问题，以及双样本均值和中位数置换检验。
- 材料陈述的贡献
- 摘要称，某些单样本问题即使总体不对称仍可渐近有效；双样本均值检验一般需等样本量，中位数检验等样本量仍可能无效。
- 阅读关注点
- 核对各类检验的具体构造、抽样与分布条件，以及等样本量结论的范围，区分有限样本精确性和渐近有效性。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；各结论的完整条件未给出，不能将等样本量视为任意置换检验有效的充分保证。
原文摘要
Fisher's randomization construction of hypothesis tests is a powerful tool to yield tests that are nonparametric in nature in that their level is exactly equal to the nominal level in finite samples over a wide range of distributional assumptions. For example, the usual permutation t test to test equality of means is valid without a normality assumption of the underlying populations. On the other hand, Fisher's randomization construction is not applicable in this example unless the underlying populations differ only in location. In general, the basis for the randomization construction is invariance of the probability distribution of the data under a transformation group. It is the goal of this article to understand the robustness properties of randomization tests by studying their asymptotic validity in situations where the basis for their construction breaks down. Here, asymptotic validity refers to whether the probability of a Type I error tends asymptotically to the nominal level. In particular, it is shown that the randomization construction is generally asymptotically valid for certain one-sample problems, such as for testing a mean or a median, even when the underlying population is not symmetric. In contrast, the randomization construction for two-sample problems may yield invalid tests, though it depends on the precise nature of the problem. For example, the two-sample permutation test based on sample means is generally asymptotically valid only if the samples are of the same size. When comparing medians, however, the two-sample permutation test is generally invalid even if the sample sizes are equal.