Higher criticism: $p$-values and criticism

By Jian Li, David O. Siegmund. 2014

59 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/edbd1cc2bf3a75eade28fb466c36294b5f2f7102

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In Artificial Intelligence

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Citations in the corpus

On the exact Berk-Jones statistics and their p-value calculation (2013, methodology): “For other examples involving real data and concrete applications, see Aldor-Noiman et al. (2014); Li and Siegmund (2015); Kaplan and Goldman (2014).”