El Llegat de Galton, Pearson, Fréchet i d'altres: com mesurar i interpretar l'associació estadística

Abstract

Along three parts, we present the concepts of correlation and statistical association, starting with Galtons notion of correlation, improved by Pearson. As an illustration, we use the classic data of Galton and Pearson on heritability of parents and children regarding the stature. The second part explains how to study the same data from a multivariate perspective (canonical correlation analysis, correspondence analysis). We also use data from Fisher. We show how to associate general data sets with distances. The third part is devoted to the bivariate distributions. We present the theory of eigenfunctions and eigenvalues for two kernels, which is applied to the diagonal expansion of a bivariate distribution, including continuous expansions in terms of integrals. We propose a family of canonical copulas, which can generate bivariate distributions.