Robustness analysis of three classical correlation coefficients under contaminated Gaussian Model

In this paper, we derive the closed-form expectations of three classical correlation coefficients, i.e., Pearson׳s product moment correlation coefficient (PPMCC), Kendall׳s tau (KT) and Spearman׳s rho (SR), under a specific contaminated Gaussian Model (CGM) that simulates a frequently encountered scenario in statistical signal processing. Theoretical and empirical results reveal the advantages of SR and KT over the PPMCC when one variable is clean and the other corrupted by a tiny fraction of impulsive noise. The newly explored theoretical and simulational findings shed new light on the topic of correlation theory which is widely applied in statistical signal processing.