Open Access
2020 Interactive martingale tests for the global null
Boyan Duan, Aaditya Ramdas, Sivaraman Balakrishnan, Larry Wasserman
Electron. J. Statist. 14(2): 4489-4551 (2020). DOI: 10.1214/20-EJS1790


Global null testing is a classical problem going back about a century to Fisher’s and Stouffer’s combination tests. In this work, we present simple martingale analogs of these classical tests, which are applicable in two distinct settings: (a) the online setting in which there is a possibly infinite sequence of $p$-values, and (b) the batch setting, where one uses prior knowledge to preorder the hypotheses. Through theory and simulations, we demonstrate that our martingale variants have higher power than their classical counterparts even when the preordering is only weakly informative. Finally, using a recent idea of “masking” $p$-values, we develop a novel interactive test for the global null that can take advantage of covariates and repeated user guidance to create a data-adaptive ordering that achieves higher detection power against structured alternatives.


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Boyan Duan. Aaditya Ramdas. Sivaraman Balakrishnan. Larry Wasserman. "Interactive martingale tests for the global null." Electron. J. Statist. 14 (2) 4489 - 4551, 2020.


Received: 1 December 2019; Published: 2020
First available in Project Euclid: 31 December 2020

MathSciNet: MR4194269
Digital Object Identifier: 10.1214/20-EJS1790

Primary: 60G10 , 62M07

Keywords: data carving , global null , Interactive testing

Vol.14 • No. 2 • 2020
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