Anomaly Detection for a Large Number of Streams: A Permutation-Based Higher Criticism Approach

Ivo V. Stoepker (Corresponding author), Rui M. Castro, Ery Arias-Castro, Edwin van den Heuvel

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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 nonparametric 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 content uniformity of an active ingredient for a batch-produced drug product. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)461-474
Number of pages14
JournalJournal of the American Statistical Association
Issue number545
Early online date16 Nov 2022
Publication statusPublished - 2024


  • Distribution-free testing
  • Minimax hypothesis testing
  • Permutation test


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