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An asymptotically exact multiple testing procedure under dependence

Author

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  • Datta, Swarnadeep
  • Dey, Monitirtha

Abstract

We propose a simple single-step multiple testing procedure that asymptotically controls the family-wise error rate (FWER) at the desired level exactly under the equicorrelated multivariate Gaussian setup. The method is shown to be asymptotically exact using an explicit plug-in estimator for the equicorrelation, and does not require stepwise adjustments. We establish its theoretical properties, including the convergence to the desired error level (along with an estimate of the rate of convergence), and demonstrate its effectiveness through simulation results. We also spell out related extensions to unknown equicorrelation, block-correlated structures and generalized FWER control.

Suggested Citation

  • Datta, Swarnadeep & Dey, Monitirtha, 2026. "An asymptotically exact multiple testing procedure under dependence," Statistics & Probability Letters, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:stapro:v:230:y:2026:i:c:s0167715225002548
    DOI: 10.1016/j.spl.2025.110609
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    References listed on IDEAS

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    1. Monitirtha Dey, 2024. "On limiting behaviors of stepwise multiple testing procedures," Statistical Papers, Springer, vol. 65(9), pages 5691-5717, December.
    2. Das, Nabaneet & Bhandari, Subir Kumar, 2021. "Bound on FWER for correlated normal," Statistics & Probability Letters, Elsevier, vol. 168(C).
    3. Dey, Monitirtha & Bhandari, Subir Kumar, 2023. "FWER goes to zero for correlated normal," Statistics & Probability Letters, Elsevier, vol. 193(C).
    4. Delattre, S. & Roquain, E., 2011. "On the false discovery proportion convergence under Gaussian equi-correlation," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 111-115, January.
    5. Das, Nabaneet & Bhandari, Subir Kumar, 2025. "FWER for normal distribution in nearly independent setup," Statistics & Probability Letters, Elsevier, vol. 219(C).
    6. Monitirtha Dey & Subir Kumar Bhandari, 2024. "Bounds on generalized family-wise error rates for normal distributions," Statistical Papers, Springer, vol. 65(4), pages 2313-2326, June.
    Full references (including those not matched with items on IDEAS)

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