Comparing dependent robust correlations

Abstract

Let r₁ and r₂ be two dependent estimates of Pearson's correlation. There is a substantial literature on testing H₀ : ρ₁ = ρ₂ , the hypothesis that the population correlation coefficients are equal. However, it is well known that Pearson's correlation is not robust. Even a single outlier can have a substantial impact on Pearson's correlation, resulting in a misleading understanding about the strength of the association among the bulk of the points. A way of mitigating this concern is to use a correlation coefficient that guards against outliers, many of which have been proposed. But apparently there are no results on how to compare dependent robust correlation coefficients when there is heteroscedasicity. Extant results suggest that a basic percentile bootstrap will perform reasonably well. This paper reports simulation results indicating the extent to which this is true when using Spearman's rho, a Winsorized correlation or a skipped correlation.

Keywords: Measures of association; Spearman's rho; Winsorized correlation; heteroscedasticity; level robust methods; skipped correlation.