Seminar by Dr. Guanxun LI, Department of Statistics, Beijing Normal University (Zhuhai)

Motivated by recent findings in Li and Zhang (2025), which establish an equivalence between certain p-value–based multiple testing procedures and the e–Benjamini–Hochberg procedure, we develop a general framework for constructing new multiple testing methods via aggregation and combination of e-values. A direct aggregation or combination can yield negligible power in practice; therefore, we introduce data-dependent weighting for e-value aggregation and combination, which significantly improves the power of the resulting e–Benjamini–Hochberg procedures. Designing these weights is nontrivial and is inspired by leave-one-out analyses, a technique widely used to prove false discovery rate control in p-value–based methods. We theoretically show that the proposed e–Benjamini–Hochberg procedure, when equipped with data-dependent weights, achieve finite-sample FDR control. Building on these weights, we propose new procedures for three distinct scenarios: (i) assembling e-values obtained from different data subsets, with simultaneous control of group-wise and overall FDRs; (ii) aggregating e-values produced by different procedures; and (iii) adaptive multiple testing methods that incorporate external structural information to increase power. Numerical studies demonstrate the effectiveness and advantages of the proposed methods in each application scenario.

Dr. Guanxun Li is an Assistant Professor in the Department of Statistics at Beijing Normal University, Zhuhai Campus. He earned his Ph.D. in Statistics from Texas A&M University in 2022. His research focuses on multiple testing, watermarking in large language models, Bayesian computation, and biostatistics.