Asymptotic properties of Pearson's rank-variate correlation coefficient under contaminated Gaussian model.
Bottom Line:
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).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.
View Article:
PubMed Central - PubMed
Affiliation: Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong, China.
ABSTRACT
Show MeSH
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. |
Related In:
Results -
Collection
License getmorefigures.php?uid=PMC4230981&req=5
Mentions: Figure 2. verifies the correctness of the variance of PRVCC, by plotting the simulation results (circles) and the theoretical results of (22) (solid lines) concerning in the same scenarios as in Figure 1. For the purpose of comparison, the contamination-free version (50) (dashed lines) is also included in each subplot to highlight the effects of and . Note that we have multiplied by for a better visual effect. This figure shows good agreements between the simulation results and the corresponding theoretical ones. Moreover, it is seen that when , the curves are symmetric and the magnitude of increase with , especially for large. On the other hand, when , the curves are no longer asymmetric. Specifically, for large, increases if and have opposite signs; and it decreases if and have the same signs. When is fixed, is the reversal of . |
View Article: PubMed Central - PubMed
Affiliation: Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong, China.