Spearman's footrule and Gini's gamma: a review with complements

Abstract

The scattered literature on Spearman's footrule and Gini's gamma is surveyed. The following topics are covered: finite-sample moments and asymptotic distribution under independence; large-sample distribution under arbitrary alternatives; asymptotic relative efficiency for testing independence; consistent asymptotic variance estimation through the jackknife; multivariate generalisations and uses. Complementary results and an extensive bibliography are provided, along with several original illustrations.

Keywords:

• asymptotic relative efficiency
• concordance
• copula
• Gini's gamma
• jackknife
• Spearman's footrule
• Spearman's rho
• ranks
• test of independence

Acknowledgements

Funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada, the Fonds québécois de la recherche sur la nature et les technologies and the Institut de finance mathématique de Montréal.