检验的检测一致性
Detection coherence of tests
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中文总结 AI 辅助
本文提出评估检验检测一致性的框架，发现部分常用非参数检验检测不一致，部分检验普遍检测一致，检测不一致的检验会遗漏或产生虚假发现，应被摒弃。
中文摘要 AI 辅助
存在一些检验，其在比检验统计量所隐含的原假设更窄的原假设下进行校准，该更窄的原假设集合被称为检测原集合。检测原集合中不属于原假设的部分是检验的盲区。本文引入了一种评估检测一致性的框架，即检验的盲区是否为空，该框架基于校准统计量、检测器、检测泛函、检测原集合和盲区等新概念构建。研究表明，Wilcoxon-Mann-Whitney、Kruskal-Wallis、Friedman 和 logrank 检验作为无限制检验是检测不一致的。检测不一致的检验在能使盲区为空的限制下可能变得一致，但在实践中，领域限制并非实现一致性的可靠途径。Kolmogorov-Smirnov、Zaremba 检验以及使用特征核的 Maximum Mean Discrepancy 检验被证明是普遍检测一致的。由于盲区的存在，检测不一致的检验在不拒绝时会遗漏发现，在拒绝时会产生虚假发现，这两种情况均与样本量无关。检测不一致的检验应当被摒弃。
英文摘要
There exist tests calibrated under a null narrower than the one implied by their test statistic -- the detection-null set. The part of the detection-null set not in the null is the test's blind spot. A framework for assessing detection coherence -- whether a test's blind spot is empty -- is introduced, built on new concepts of calibration statistic, detector, detection functional, detection-null set, and blind spot. It is demonstrated that the Wilcoxon--Mann--Whitney, Kruskal--Wallis, Friedman, and logrank tests are detection incoherent as unrestricted tests. Detection incoherent tests may become coherent under restrictions that make the blind spot empty, though domain restriction is not a reliable route to coherence in practice, since the boundary of the coherence-restoring domain is unknown and unverifiable. The Kolmogorov--Smirnov and Zaremba tests, and the Maximum Mean Discrepancy test with a characteristic kernel, are shown to be universally detection coherent. Due to the blind spot, a detection incoherent test misses discoveries when non-rejecting and yields spurious discoveries when rejecting, in both cases regardless of sample size. Detection incoherent tests should be abandoned.
发表机构
- Comenius University in Bratislava（布拉迪斯拉发康斯坦丁尼大学）
- Institute of Measurement Science, Slovak Academy of Sciences（斯洛伐克科学院测量科学研究所）
- Bioptic Laboratory Ltd.（Bioptic实验室有限公司）
机构由 AI 辅助整理，请以论文原文为准。
