A coordinate-free approach to testable hypotheses

Abstract

Using the coordinate-free version of the linear model and geometrical considerations, the usual definition of testable hyptheses is extended. The concept of partially testable hypotheses is defined in that context. This new approach provides an alternative to the one given by Peixoto (1986), offering some complementary aspects. Simple and direct techniques for testing the new testable hyptheses by means of the classical testing procedure are given.

Keywords:

• estimable functions
• geometrical methodology
• non-full rank models
• partially testable hypotheses