Propositions, Principles and Methods: The Linear Hypothesis and Structural Change

This paper seeks to distinguish between principles upon which testing of statistical hypotheses may be based and the practical methods which these principles generate. Seber's (1964) conclusion, that the Wald, Lagrange Multiplier and Likelihood Ratio Principles all lead to the same test statistic for a linear hypothesis is re-examined. Simple relations between various test statistics are their distributions are outlined. These are applied to two well-known methods of testing structural change.