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

TL;DR

This paper introduces two new estimators for multivariate Spearman's footrule, compares them with existing methods, and analyzes their efficiency and performance in small samples for testing multivariate independence.

Contribution

The paper proposes two novel estimators for multivariate Spearman's footrule based on Average Orthant Dependence measures, enhancing small-sample performance.

Findings

New estimators outperform existing ones in small samples.

All estimators are asymptotically equivalent.

Proposed estimators show favorable Pitman efficiency.

Abstract

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 and 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.