Asymptotic properties of Pearson's rank-variate correlation coefficient under contaminated Gaussian model

Rubao Ma; Weichao Xu; Yun Zhang; Zhongfu Ye

doi:10.1371/journal.pone.0112215

Asymptotic properties of Pearson's rank-variate correlation coefficient under contaminated Gaussian model

PLoS One. 2014 Nov 13;9(11):e112215. doi: 10.1371/journal.pone.0112215. eCollection 2014.

Authors

Rubao Ma¹, Weichao Xu¹, Yun Zhang¹, Zhongfu Ye²

Affiliations

¹ Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong, China.
² Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, Anhui, China.

Abstract

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Models, Statistical*
Monte Carlo Method
Normal Distribution
Statistics, Nonparametric*

Grants and funding

This work was supported in part by National Natural Science Foundation of China (Project 61271380), in part by Guangdong Natural Science Foundation (Project S2012010009870), in part by 100-Talents Scheme Funding from Guangdong University of Technology (Grant 112418006), in part by the Talent Introduction Special Funds from Guangdong Province (Grant 2050205), in part by a team project from Guangdong University of Technology (Grant GDUT2011-07), and Project Program of Key Laboratory of Guangdong Higher Education Institutes of China (Grant 2013CXZDA015). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.