Open Access
May 2020 Agnostic tests can control the type I and type II errors simultaneously
Victor Coscrato, Rafael Izbicki, Rafael B. Stern
Braz. J. Probab. Stat. 34(2): 230-250 (May 2020). DOI: 10.1214/19-BJPS431


Despite its common practice, statistical hypothesis testing presents challenges in interpretation. For instance, in the standard frequentist framework there is no control of the type II error. As a result, the non-rejection of the null hypothesis $(H_{0})$ cannot reasonably be interpreted as its acceptance. We propose that this dilemma can be overcome by using agnostic hypothesis tests, since they can control the type I and II errors simultaneously. In order to make this idea operational, we show how to obtain agnostic hypothesis in typical models. For instance, we show how to build (unbiased) uniformly most powerful agnostic tests and how to obtain agnostic tests from standard p-values. Also, we present conditions such that the above tests can be made logically coherent. Finally, we present examples of consistent agnostic hypothesis tests.


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Victor Coscrato. Rafael Izbicki. Rafael B. Stern. "Agnostic tests can control the type I and type II errors simultaneously." Braz. J. Probab. Stat. 34 (2) 230 - 250, May 2020.


Received: 1 June 2018; Accepted: 1 January 2019; Published: May 2020
First available in Project Euclid: 4 May 2020

zbMATH: 07232927
MathSciNet: MR4093257
Digital Object Identifier: 10.1214/19-BJPS431

Keywords: hypothesis test , logical consistency , three-decision problem , uniformly most powerful tests

Rights: Copyright © 2020 Brazilian Statistical Association

Vol.34 • No. 2 • May 2020
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