Test statistics and p-values

TL;DR

This paper broadens the concept of test statistics in hypothesis testing, proposing a more general and arguably maximal framework within the context of simple hypotheses.

Contribution

It introduces a generalized notion of test statistics that extends beyond traditional definitions for simple hypotheses.

Findings

Proposes a natural, maximal generalization of test statistics.

Clarifies limitations of traditional test statistic concepts.

Focuses on simple hypotheses for the theoretical development.

Abstract

We point out that the traditional notion of test statistic is too narrow, and we propose a natural generalization that is arguably maximal. The study is restricted to simple statistical hypotheses.