Robust mean change point testing in high-dimensional data with heavy tails

Mengchu Li, Yudong Chen, Tengyao Wang and Yu Yi

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We study mean change point testing problems for high-dimensional data, with exponentially- or polynomially-decaying tails. In each case, depending on the ℓ0-norm of the mean change vector, we separately consider dense and sparse regimes. We characterise the boundary between the dense and sparse regimes under the above two tail conditions for the first time in the change point literature and propose novel testing procedures that attain optimal rates in each of the four regimes up to a poly-iterated logarithmic factor. To be specific, when the error distributions possess exponentially-decaying tails, a near-optimal CUSUM-type statistic is considered. As for polynomially-decaying tails, admitting bounded α-th moments for some α ≥ 4, we introduce a median-of-means-type test statistic that achieves a near-optimal testing rate in both dense and sparse regimes. Our investigation in the even more challenging case of 2 ≤ α

Keywords: change points; heavy-tailed error; minimax testing; high-dimensional data; robustness (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2026-01-05
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Published in IEEE Transactions on Information Theory, 5, January, 2026, 72(1), pp. 571 - 609. ISSN: 0018-9448

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:130166

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