Gini's ideas: new perspectives for modern multivariate statistical analysis

Corrado Gini (1884-1964) may be considered the greatest Italian statistician. We believe that his important contributions to statistics, however mainly limited to the univariate context, may be profitably employed in modern multivariate statistical methods, aimed at overcoming the curse of dimensionality by decomposing multivariate problems into a series of suitably posed univariate ones. In this paper we critically summarize Gini’s proposals and consider their impact on multivariate statistical methods, both reviewing already well established applications and suggesting new perspectives. Particular attention will be devoted to classification and regression trees, multiple linear regression, linear dimension reduction methods and transvariation based discrimination.