Nonparametric estimation of the multivariate Spearman's footrule: A further discussion

In this paper, we propose two new estimators of the multivariate rank correlation coefficient Spearman's footrule which are based on two general estimators for Average Orthant Dependence measures. We compare the new proposals with a previous estimator existing in the literature , show that the three estimators are asymptotically equivalent, but, in small samples, one of the proposed estimators outperforms the others. We also analyse Pitman efficiency of these indices to test for multivariate independence as compared to multivariate versions of Kendall's tau and Spearman's rho.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).

Automated summary

In this paper, two new estimators for the multivariate rank correlation coefficient Spearman's footrule are proposed based on two general estimators. The new proposals are compared with an existing estimator in the literature and it is shown that the three estimators are asymptotically equivalent. However, in small samples, one of the proposed estimators outperforms the others. The Pitman efficiency of these indices to test for multivariate independence is also analyzed compared to multivariate versions of Kendall's tau and Spearman's rho.