# Higher criticism: p-values and criticism

arXiv: https://arxiv.org/abs/1411.1437 · HTML: https://mlsanity.com/paper/1411.1437/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2014.

## Built on by (most cited first, 2 of 2)

- [Debiasing Watermarks for Large Language Models via Maximal Coupling](https://mlsanity.com/paper/2411.11203/) (2024)
- [Everywhere Valid Bounds on False Discovery Proportions in Conformal Inference](https://mlsanity.com/paper/2605.20726/) (2026)

## Abstract (arXiv)

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.