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June 2015 Higher criticism: $p$-values and criticism
Jian Li, David Siegmund
Ann. Statist. 43(3): 1323-1350 (June 2015). DOI: 10.1214/15-AOS1312


This paper compares the higher criticism statistic (Donoho and Jin [ Ann. Statist. 32 (2004) 962–994]), a modification of the higher criticism statistic also suggested by Donoho and Jin, and two statistics of the Berk–Jones [ Z. Wahrsch. Verw. Gebiete 47 (1979) 47–59] type. New approximations to the significance levels of the statistics are derived, and their accuracy is studied by simulations. By numerical examples it is shown that over a broad range of sample sizes the Berk–Jones statistics have a better power function than the higher criticism statistics to detect sparse mixtures. The applications suggested by Meinshausen and Rice [ Ann. Statist. 34 (2006) 373–393], to find lower confidence bounds for the number of false hypotheses, and by Jeng, Cai and Li [ Biometrika 100 (2013) 157–172], to detect copy number variants, are also studied.


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Jian Li. David Siegmund. "Higher criticism: $p$-values and criticism." Ann. Statist. 43 (3) 1323 - 1350, June 2015.


Received: 1 January 2014; Revised: 1 October 2014; Published: June 2015
First available in Project Euclid: 15 May 2015

zbMATH: 1320.62039
MathSciNet: MR3346705
Digital Object Identifier: 10.1214/15-AOS1312

Primary: 62F10
Secondary: 62G20

Keywords: Global $p$-value , sparse mixture

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 3 • June 2015
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