On the Expressions of Estimability in Testing General Linear Hypotheses

Abstract

In testing a general linear hypothesis of the form K ′β ∊ ( W ′) under a general linear model, an equivalent hypothesis involving only estimable parametric functions is provided, and then an explicit test statistic in terms of the model matrices is given. The corresponding results are expanded to the case of a general linear model with a restriction and are illustrated by an example.

Keywords:

• Equivalent general linear hypotheses
• Estimability
• Estimable functions
• General linear models
• Testable hypothesis

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62H15

Acknowledgments

The authors are grateful to the referee and to the editor for their very helpful suggestions, which led to the improved version of this paper.