Correspondence analysis and diagonal expansions in terms of distribution functions

Abstract

Correspondence analysis on two categorical variables is usually formulated on a two-way contingency table of frequencies. Assuming the variables to be ordinal and re-expressing the canonical correlation analysis, we show that correspondence analysis may also be approached in terms of the cumulative frequencies. A continuous extension is made. It is shown that the diagonal expansion of a bivariate density may be formulated using integral operators on the cumulative distribution function.