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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.

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The numerical verification of (22), the variance 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 (50) is also posted together (see dashed curves).
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pone-0112215-g002: The numerical verification of (22), the variance 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 (50) is also posted together (see dashed curves).

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 .


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 (22), the variance 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 (50) 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-g002: The numerical verification of (22), the variance 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 (50) is also posted together (see dashed curves).
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 .

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