The exact power function of an exact test of a regression model against multiple separate alternatives

Abstract

A common procedure for testing a regression model against separate alternatives is to check the statistical significance of predictions from the latter appended as artificial regressors in the model under test. This paper derives the previously-unknown exact small-sample power function of such a procedure. It is then demonstrated that the procedure is biased in small samples.

Keywords:

• exact tests
• separate regressions
• power function
• doubly-noneentral F distribution
• bias