Admissibility of Test Procedures for Linear Hypotheses in General Linear Model

Abstract

This article shows that an F-test procedure is admissible for testing a linear hypothesis concerning one of the split mean vectors in a general linear model and an F-test procedure is also admissible for testing a linear hypothesis concerning another of the split mean vectors in the same model. These results are proved by showing that the critical functions of the tests are unique Bayes procedures with respect to proper prior distributions set in common for the null hypotheses and for the alternative ones, respectively.

Keywords:

• Bayes test procedures
• Covariance matrix structure
• Likelihood ratio tests
• Proper prior distributions
• Split mean vectors
• UMPI F-test procedures

Mathematics Subject Classification:

• Primary 62C15
• Secondary 62H15