Enhanced Rank-Based Correlation Estimation Using Smoothed Wilcoxon Rank Scores

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.