Higher criticism: $p$-values and criticism
Abstract
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.
Cite
@article{arxiv.1411.1437,
title = {Higher criticism: $p$-values and criticism},
author = {Jian Li and David Siegmund},
journal= {arXiv preprint arXiv:1411.1437},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.1214/15-AOS1312 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)