Enhanced Rank-Based Correlation Estimation Using Smoothed Wilcoxon Rank Scores

TL;DR

This paper introduces a smoothed Wilcoxon rank score method to improve Spearman's rank correlation estimation, effectively handling ties and increasing efficiency in monotone association detection.

Contribution

It presents a novel smoothed rank-based estimator for Spearman's correlation, enhancing tie handling and efficiency over traditional methods.

Findings

The new estimator outperforms traditional Spearman's rho in simulations.

The method effectively handles tied data.

Asymptotic properties are established for the estimator.

Abstract

This article proposes an improved version of the Spearman rank correlation based on using Wilcoxon rank score function. A smoothed empirical cumulative distribution function (ecdf)computes the smoothed ranks and replaces the regular ranks in the Wilcoxon rank score function. The smoothed Wilcoxon rank scores are then used for estimation of the Spearman's correlation. The proposed approach is similar to the Spearman's rho estimator which uses ranks of the random samples of X and Y but the proposed method improves Spearman's approach such as handling ties and gaining higher efficiency under monotone associations. A Wald type hypothesis test has been proposed for the new estimator and the asymptotic properties are shown.