ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
Multiple testing procedures under positive dependency with block structure
Provisionally accepted
- 1Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria
- 2Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (BAS), Sofia, Bulgaria
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The classical Benjamini-Hochberg (B-H) method, widely used across various disciplines such as genetics, epidemiology, and social sciences, serves as an established procedure for controlling the false discovery rate (FDR) in multiple comparison scenarios. The B-H method assumes independence among tests, which often does not hold in large-scale dependent datasets. The Benjamini-Yekutieli (B-Y) adjustment controls the FDR under arbitrary dependence but is often very conservative and can lead to a reduction in statistical power. This paper investigates the performance of the B-H and B-Y procedures under specific positive block dependence structures. Two parametric forms of block dependence are considered to model the correlation among paired $t$-test statistics. Estimation algorithms induced by different matrix norms are developed for approximating the value of the unknown parameter. Modifications of existing multiple testing approaches are proposed by incorporating test dependence and enhancing their power through integration of Kolmogorov-Smirnov tests. Simulation studies are performed to demonstrate that the recommended methods preserve FDR control while improving power compared to traditional techniques.
Keywords: Benjamini-Hochberg procedure, Benjamini-Yekutieli adjustment, false discovery rate, Kolmogorov-smirnov test, multiple comparisons, P-values, statistical power
Received: 17 Nov 2025; Accepted: 28 Jan 2026.
Copyright: © 2026 Nikolov, Savov and Palejev. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Nikolay I. Nikolov
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