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arXiv · 2607.29507

Adversarially robust multiple testing in high dimensions

Anders Bredahl Kock·David Preinerstorfer
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Abstract

Robust multiple testing procedures for assessing equality restrictions on the coordinates of high-dimensional mean vectors are proposed. Our procedures are based on quantile-winsorization techniques, approximately control the familywise error rate (strongly) under adversarial contamination, and allow the number of hypotheses to grow exponentially with sample size, despite requiring only slightly more than two moments. Technically, our one-sample results build on recent Gaussian approximation inequalities for the distribution of high-dimensional quantile-winsorized means, whereas our two-sample results are based on extensions thereof, which we develop here and which could be of some interest in their own right.

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Anders Bredahl Kock, David Preinerstorfer. 2026-07-31. Adversarially robust multiple testing in high dimensions. https://arxiv.org/abs/2607.29507

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