Asymptotic Properties of Pearson's Rank-Variate Correlation Coefficient under Contaminated Gaussian Model

作者：Ma, Rubao; Xu, Weichao^*; Zhang, Yun; Ye, Zhongfu

来源：PLos One, 2014, 9(11): UNSP e112215.

DOI：10.1371/journal.pone.0112215

This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.

• 出版日期2014-11-13
• 单位广东工业大学; 中国科学技术大学