The Annals of Applied Statistics

Hypothesis testing for high-dimensional multinomials: A selective review

Sivaraman Balakrishnan and Larry Wasserman

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Abstract

The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the $\chi^{2}$-test and the likelihood ratio test can have poor power in the high-dimensional setting. Much of the research in this area has focused on finding tests with asymptotically normal limits and developing (stringent) conditions under which tests have normal limits. We argue that this perspective suffers from a significant deficiency: it can exclude many high-dimensional cases when—despite having non-normal null distributions—carefully designed tests can have high power. Finally, we illustrate that taking a minimax perspective and considering refinements of this perspective can lead naturally to powerful and practical tests.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 2 (2018), 727-749.

Dates
Received: December 2017
Revised: February 2018
First available in Project Euclid: 28 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1532743474

Digital Object Identifier
doi:10.1214/18-AOAS1155SF

Mathematical Reviews number (MathSciNet)
MR3834283

Keywords
Hypothesis testing high-dimensional multinomials

Citation

Balakrishnan, Sivaraman; Wasserman, Larry. Hypothesis testing for high-dimensional multinomials: A selective review. Ann. Appl. Stat. 12 (2018), no. 2, 727--749. doi:10.1214/18-AOAS1155SF. https://projecteuclid.org/euclid.aoas/1532743474


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