Agnostic tests can control the type I and type II errors simultaneously

Abstract

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 (H0) 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.

Publication
In Brazilian Journal of Probability and Statistics
Rafael B. Stern
Rafael B. Stern
Professor of Statistics

I am an Assistant Professor at the Federal University of São Carlos. I have a B.A. in Statistics from University of São Paulo, a B.A. in Law from Pontifícia Universidade Católica in São Paulo, and a Ph.D. in Statistics from Carnegie Mellon University. I am currently a member of the Scientific Council of the Brazilian Association of Jurimetrics, an associate investigator at NeuroMat and a member of the Order of Attorneys of Brazil.