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On Large-Scale Multiple Testing Over Networks: A Non-Asymptotic Approach

arXiv · AI, language, vision and robotics · article · Sep 12, 2026 · UTC

Distributed multiple testing asks $N$ sites to control a global false discovery rate (FDR) under a tight communication budget. The greedy interval-aggregation algorithm of Pournaderi and Xiang (2024) solves this asymptotically but can violate $\mathrm{FDR}\leα$ at finite samples. We trace the violation to a winner's-curse bias in the selected density statistics, of exact order $Θ(m^{-1/4}\sqrt{\log m})$ at the standard bandwidth $\varepsilon\asymp m^{-1/2}$, with $m$ the total number of p-values in the network. Cross-Fit Greedy Aggregation (CFGA) eliminates the curse by selecting the nested re

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