Order Statistics Correlation Coefficient as a Novel Association Measurement With Applications to Biosignal Analysis

Abstract

In this paper, we propose a novel correlation coefficient based on order statistics and rearrangement inequality. The proposed coefficient represents a compromise between the Pearson's linear coefficient and the two rank-based coefficients, namely Spearman's rho and Kendall's tau. Theoretical derivations show that our coefficient possesses the same basic properties as the three classical coefficients. Experimental studies based on four models and six biosignals show that our coefficient performs better than the two rank-based coefficients when measuring linear associations; whereas it is well able to detect monotone nonlinear associations like the two rank-based coefficients. Extensive statistical analyses also suggest that our new coefficient has superior anti-noise robustness, small biasedness, high sensitivity to changes in association, accurate time-delay detection ability, fast computational speed, and robustness under monotone nonlinear transformations.