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

Ma R, Xu W, Zhang Y, Ye Z - PLoS ONE (2014)

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
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.

Show MeSH
The numerical verification of (21), the expectation of  in Theorem 1.The number of samples is chose as . In the vertically up direction,  is decreasing following  respectively; whereas  corresponds to a increasing trend in the horizontally right direction, following  respectively. It shows a good agreement between the simulation result (circles) and the theoretical computation (solid lines) in each subplot. As a reference, the contamination-free version (49) is also posted together (see dashed curves).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4230981&req=5

pone-0112215-g001: The numerical verification of (21), the expectation of in Theorem 1.The number of samples is chose as . In the vertically up direction, is decreasing following respectively; whereas corresponds to a increasing trend in the horizontally right direction, following respectively. It shows a good agreement between the simulation result (circles) and the theoretical computation (solid lines) in each subplot. As a reference, the contamination-free version (49) is also posted together (see dashed curves).

Mentions: Figure 1. verifies the correctness of the mean of PRVCC under CGM (4) for large samples and small . Specifically, in Figure 1. we plot the simulation results (circles) and the theoretical results of (21) (solid lines), and the contamination-free version (49) (dashed lines) under different combinations of and . Good agreements are observed between the simulation results and the theoretical counterparts. It can also be observed that the larger the contamination fraction and difference between and , the bigger the bias between and the ideal dashed curve corresponding to .


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

Ma R, Xu W, Zhang Y, Ye Z - PLoS ONE (2014)

The numerical verification of (21), the expectation of  in Theorem 1.The number of samples is chose as . In the vertically up direction,  is decreasing following  respectively; whereas  corresponds to a increasing trend in the horizontally right direction, following  respectively. It shows a good agreement between the simulation result (circles) and the theoretical computation (solid lines) in each subplot. As a reference, the contamination-free version (49) is also posted together (see dashed curves).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230981&req=5

pone-0112215-g001: The numerical verification of (21), the expectation of in Theorem 1.The number of samples is chose as . In the vertically up direction, is decreasing following respectively; whereas corresponds to a increasing trend in the horizontally right direction, following respectively. It shows a good agreement between the simulation result (circles) and the theoretical computation (solid lines) in each subplot. As a reference, the contamination-free version (49) is also posted together (see dashed curves).
Mentions: Figure 1. verifies the correctness of the mean of PRVCC under CGM (4) for large samples and small . Specifically, in Figure 1. we plot the simulation results (circles) and the theoretical results of (21) (solid lines), and the contamination-free version (49) (dashed lines) under different combinations of and . Good agreements are observed between the simulation results and the theoretical counterparts. It can also be observed that the larger the contamination fraction and difference between and , the bigger the bias between and the ideal dashed curve corresponding to .

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
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.

Show MeSH