Statistical Properties of Average Kendall’s Tau Under Multivariate Contaminated Gaussian Model

Abstract

In this paper, we derived the analytical forms of the expectation and variance of average Kendall’s tau (AKT) under a specific multivariate contaminated Gaussian model (MCGM), which can simulate a scenario where the multi-channel noise exhibits an impulsive manner. For a better understanding of AKT, we compared AKT to other two classical concordance correlation coefficients, i.e., Kendall’s concordance coefficient (KCC), and the average Pearson’s product moment correlation coefficient (APPMCC) with respect to the root mean squared error (RMSE). We also applied AKT, KCC and APPMCC to the problem of multi-channel random signal detection. Monte Carlo simulations not only validated our theoretical findings, but also revealed the advantage of AKT over KCC and APPMCC in terms of the receiver operating characteristic (ROC) curves.

Keywords

• Average Kendall’s tau (AKT)
• multivariate contaminated Gaussian model (MCGM)
• root mean squared error (RMSE)
• multi-channel signal detection
• receiver operating characteristic (ROC) curve