In novelty detection, the objective is to determine whether the test sample contains any outliers, using a sample of controls (inliers). This involves many-to-one comparisons of individual test points against the control sample. A recent approach applies the Benjamini-Hochberg procedure to the conformal $p$-values resulting from these comparisons, ensuring false discovery rate control. In this paper, we suggest using Wilcoxon-Mann-Whitney tests for the comparisons and subsequently applying the closed testing principle to derive post-hoc confidence bounds for the number of outliers in any subset of the test sample. We revisit an elegant result that under a nonparametric alternative known as Lehmann's alternative, Wilcoxon-Mann-Whitney is locally most powerful among rank tests. By combining this result with a simple observation, we demonstrate that the proposed procedure is more powerful for the null hypothesis of no outliers than the Benjamini-Hochberg procedure applied to conformal $p$-values.

翻译：在新颖性检测中，目标是通过使用控制样本（内点）判断测试样本是否包含任何异常点。这涉及到将单个测试点与控制样本进行多对一比较。近期一种方法对这些比较产生的共形$p$值应用Benjamini-Hochberg过程，从而控制错误发现率。本文建议使用Wilcoxon-Mann-Whitney检验进行比较，并随后应用闭合检验原理，推导出测试样本任意子集中异常点数量的后验置信界。我们重新审视一个优雅结论：在称为Lehmann替代假设的非参数替代方案下，Wilcoxon-Mann-Whitney检验是秩检验中局部最强大的。通过将该结论与一个简单观察相结合，我们证明所提出的过程在检验无异常点的零假设时，比直接对共形$p$值应用Benjamini-Hochberg过程更具统计功效。