Translator Disclaimer
August 2020 Beyond HC: More sensitive tests for rare/weak alternatives
Thomas Porter, Michael Stewart
Ann. Statist. 48(4): 2230-2252 (August 2020). DOI: 10.1214/19-AOS1885


Higher criticism (HC) is a popular method for large-scale inference problems based on identifying unusually high proportions of small $p$-values. It has been shown to enjoy a lower-order optimality property in a simple normal location mixture model which is shared by the ‘tailor-made’ parametric generalised likelihood ratio test (GLRT) for the same model; however, HC has also been shown to perform well outside this ‘narrow’ model.

We develop a higher-order framework for analysing the power of these and similar procedures, which reveals the perhaps unsurprising fact that the GLRT enjoys an edge in power over HC for the normal location mixture model. We also identify a similar parametric mixture model to which HC is similarly ‘tailor-made’ and show that the situation is (at least partly) reversed there. We also show that in the normal location mixture model a procedure based on the empirical moment-generating function enjoys the same local power properties as the GLRT and may be recommended as an easy to implement (and interpret), complementary procedure to HC. Some other practical advice regarding the implementation of these procedures is provided. Finally, we provide some simulation results to help interpret our theoretical findings.


Download Citation

Thomas Porter. Michael Stewart. "Beyond HC: More sensitive tests for rare/weak alternatives." Ann. Statist. 48 (4) 2230 - 2252, August 2020.


Received: 1 November 2016; Revised: 1 July 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134793
Digital Object Identifier: 10.1214/19-AOS1885

Primary: 62F03
Secondary: 62F05, 62G30, 62G32

Rights: Copyright © 2020 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.48 • No. 4 • August 2020
Back to Top