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2019 Adaptive $p$-value weighting with power optimality
Guillermo Durand
Electron. J. Statist. 13(2): 3336-3385 (2019). DOI: 10.1214/19-EJS1578


Weighting the $p$-values is a well-established strategy that improves the power of multiple testing procedures while dealing with heterogeneous data. However, how to achieve this task in an optimal way is rarely considered in the literature. This paper contributes to fill the gap in the case of group-structured null hypotheses, by introducing a new class of procedures named ADDOW (for Adaptive Data Driven Optimal Weighting) that adapts both to the alternative distribution and to the proportion of true null hypotheses. We prove the asymptotical FDR control and power optimality among all weighted procedures of ADDOW, which shows that it dominates all existing procedures in that framework. Some numerical experiments show that the proposed method preserves its optimal properties in the finite sample setting when the number of tests is moderately large.


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Guillermo Durand. "Adaptive $p$-value weighting with power optimality." Electron. J. Statist. 13 (2) 3336 - 3385, 2019.


Received: 1 September 2017; Published: 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07113720
MathSciNet: MR4010982
Digital Object Identifier: 10.1214/19-EJS1578

Primary: 62J15
Secondary: 62G10


Vol.13 • No. 2 • 2019
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