On the Nuisance Parameter Elimination Principle in Hypothesis Testing

TL;DR

This paper explores a statistical principle for handling nuisance parameters in hypothesis testing and shows how a specific test can simplify the process.

Contribution

The paper proves that the mixed test follows the Non-Informative Nuisance Parameter Principle for discrete data and simplifies its application.

Findings

The mixed test obeys the Non-Informative Nuisance Parameter Principle in discrete sample spaces.

Adherence to the principle simplifies the performance of the mixed test in hypothesis testing.

New solutions for testing hypotheses with count data are demonstrated.

Abstract

The Non-Informative Nuisance Parameter Principle concerns the problem of how inferences about a parameter of interest should be made in the presence of nuisance parameters. The principle is examined in the context of the hypothesis testing problem. We prove that the mixed test obeys the principle for discrete sample spaces. We also show how adherence of the mixed test to the principle can make performance of the test much easier. These findings are illustrated with new solutions to well-known problems of testing hypotheses for count data.