Optimal tests for arbitrarily varying object and the familywise error rates

Abstract

In this article the optimal statistical hypotheses testing to make decision for arbitrarily varying object are considered. The statistician would like to control the overall error rate relative to draw statistically valid conclusions from each test. The familywise error rate (FWE) metric and the hypothesis test procedure while controlling both the type I and II FWEs are generalized by an arbitrarily varying object. The characteristics of logarithmically asymptotically optimal (LAO) hypotheses testing are studied. The purpose of research is to express the optimal functional relation among the reliabilities of LAO hypotheses testing and to judge with FWE metric.

Keywords:

• Familywise error rate
• hypotheses testing
• information theory
• reliability

2010 AMS Classification:

• Primary 62F03
• secondary 94A15

Acknowledgments

The author wish to thank the Ahvaz Branch, Islamic Azad University for the financial support. The author would like to thank all the editors and reviewers for their comments in the development and improvement of this paper.