Optimum Statistical Test Procedure

TL;DR

This paper introduces a statistical test procedure that minimizes the total error probability regardless of the knowledge of the variance, offering a unified approach for hypothesis testing.

Contribution

The paper presents a new optimal test procedure that minimizes combined error probabilities without requiring knowledge of the variance.

Findings

The test achieves minimal total error probability.

It is applicable whether the variance is known or unknown.

The method improves upon existing tests in terms of error minimization.

Abstract

In this paper we obtain a test which minimizes the sum of the two error probabilities irrespective of whether $\sigma^2$ is known or unknown.