Anomaly detection when observing a large number of data streams is essential in a variety of applications, ranging from epidemiological studies to monitoring of complex systems. High-dimensional scenarios are usually tackled with scan-statistics and related methods, requiring stringent modeling assumptions for proper calibration. In this work we take a non-parametric stance, and propose a permutation-based variant of the higher criticism statistic not requiring knowledge of the null distribution. This results in an exact test in finite samples which is asymptotically optimal in the wide class of exponential models. We demonstrate the power loss in finite samples is minimal with respect to the oracle test. Furthermore, since the proposed statistic does not rely on asymptotic approximations it typically performs better than popular variants of higher criticism that rely on such approximations. We include recommendations such that the test can be readily applied in practice, and demonstrate its applicability in monitoring the daily number of COVID-19 cases in the Netherlands.

翻译：在从流行病学研究到复杂系统监测等各种应用中,观测大量数据流时必须进行异常的探测,从流行病学研究到监测复杂系统,从各种应用到不同应用,从不同角度,从不同角度出发,观测大量数据流都是必不可少的,从不同角度处理高维假设,通常采用扫描统计和相关方法,要求为正确校准而采用严格的模型假设;在这项工作中,我们采取非参数立场,提出不要求了解无效分布的较高批评统计数据的基于变体的变体,不要求了解无效分布;这导致精确测试有限的样本,这在广泛的指数模型类别中是尽可能最佳的;我们证明,在试验中,有限样本的功率损失是最小的;此外,由于拟议的统计通常不依赖于非物质近似性近似性,其表现优于依赖这种近似性的批评的流行变体。我们提出了这样的建议,即试验可以很容易在实际中应用,并表明其在监测荷兰每日COVID-19案例的数量时的适用性。