Optimal Testing of Statistical Hypotheses and Multiple Familywise Error Rates

Abstract

This article considers the statistical hypotheses testing to make decision among hypotheses concerning many families of probability distributions. The statistician would like to control the overall error rate relative to draw statistically valid conclusions from each test, while being as efficient as possible.  Each of the  hypotheses  are tested by the familywise error (FWE) rate metric and the hypothesis test procedure while controlling both the type I and II FWEs is generalized. The proposed procedure shows simultaneous more reliability and less conservative error control relative to fixed sample and other recently proposed sequential procedures. Furthermore, description of the characteristics of logarithmically asymptotically optimal (LAO) hypotheses testing is 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.