Extensions and generalizations

Abstract

In the preceding chapter we introduced the essential ingredients of the theory of canonical correlation. The theory stems from the work of Hotelling in the 1930s. Since Hotelling’s pioneering studies the theory has been added to in a number of ways. The present chapter deals with developments of this kind. We shall begin by considering several numerical indices which have been devised in order to further the interpretation of results in addition to the canonical correlations, weights and variates of the classical solution. Other developments are directed towards widening the applicability of the original theory and several generalizations of this kind will be mentioned. Tests of statistical hypotheses are sometimes of interest in canonical analysis and the chapter closes with an account of hypothesis testing.