ON UMP INVARIANT F-TEST PROCEDURES IN A GENERAL LINEAR MODEL

Abstract

A simple method of setting linear hypotheses for a split mean vector testable by F-tests in a general linear model, when the covariance matrix has a general form and is completely unknown, is provided by extending the method discussed in Ukita et al. The critical functions in these F-tests are constructed as UMP invariants, when the covariance matrix has a known structure. Further critical functions in F-tests of linear hypotheses for the other split mean vector in the model are shown to be UMP invariant if the same known structure of the covariance matrix is assumed.

Keywords:

• Setting linear hypotheses
• Split mean vectors
• Invariant critical functions
• Maximal invariants under transformation groups
• Known structure of covariance matrix

Acknowledgments