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Asymptotic mean and variance of Gini correlation for bivariate normal samples

Asymptotic mean and variance of Gini correlation for bivariate normal samples
Asymptotic mean and variance of Gini correlation for bivariate normal samples
This paper derives the asymptotic analytical forms of the mean and variance of the Gini correlation (GC) with respect to samples drawn from bivariate normal populations. The asymptotic relative efficiency (ARE) of the Gini correlation to Pearson's product moment correlation coefficient (PPMCC) is investigated under the normal assumptions. To gain further insight into GC, we also compare the Gini correlation to other two closely related correlation coefficients, namely, the order statistics correlation coefficient (OSCC) and Spearman's rho (SR). Theoretical and simulation results suggest that the performance of GC lies in between those of OSCC and SR when estimating the correlation coefficient of the bivariate normal population. The newly found theoretical results along with other desirable properties enable GC to be a useful alternative to the existing coefficients, especially when one wants to make a trade-off between the efficiency and robustness to monotone nonlinearity.
1053-587X
522-534
Xu, Weichao
b6a6815b-8ed4-41a0-8ee1-943d1e804d1a
Hung, Y.S.
e15ca65e-ebd8-469d-8792-0e139040ff68
Niranjan, M.
5cbaeea8-7288-4b55-a89c-c43d212ddd4f
Shen, M.F.
1c08e7b3-2c44-4f46-853a-40803328afdc
Xu, Weichao
b6a6815b-8ed4-41a0-8ee1-943d1e804d1a
Hung, Y.S.
e15ca65e-ebd8-469d-8792-0e139040ff68
Niranjan, M.
5cbaeea8-7288-4b55-a89c-c43d212ddd4f
Shen, M.F.
1c08e7b3-2c44-4f46-853a-40803328afdc

Xu, Weichao, Hung, Y.S., Niranjan, M. and Shen, M.F. (2010) Asymptotic mean and variance of Gini correlation for bivariate normal samples IEEE Transactions on Signal Processing, 58, (2), pp. 522-534. (doi:10.1109/TSP.2009.2032448).

Record type: Article

Abstract

This paper derives the asymptotic analytical forms of the mean and variance of the Gini correlation (GC) with respect to samples drawn from bivariate normal populations. The asymptotic relative efficiency (ARE) of the Gini correlation to Pearson's product moment correlation coefficient (PPMCC) is investigated under the normal assumptions. To gain further insight into GC, we also compare the Gini correlation to other two closely related correlation coefficients, namely, the order statistics correlation coefficient (OSCC) and Spearman's rho (SR). Theoretical and simulation results suggest that the performance of GC lies in between those of OSCC and SR when estimating the correlation coefficient of the bivariate normal population. The newly found theoretical results along with other desirable properties enable GC to be a useful alternative to the existing coefficients, especially when one wants to make a trade-off between the efficiency and robustness to monotone nonlinearity.

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More information

e-pub ahead of print date: 18 September 2009
Published date: February 2010
Additional Information: Imported from ISI Web of Science
Organisations: Southampton Wireless Group

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Local EPrints ID: 270723
URI: http://eprints.soton.ac.uk/id/eprint/270723
ISSN: 1053-587X
PURE UUID: 8e5c9356-24f8-4f2d-99f9-10eb4fc258e4

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Date deposited: 21 Apr 2010 07:46
Last modified: 18 Jul 2017 06:51

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Contributors

Author: Weichao Xu
Author: Y.S. Hung
Author: M. Niranjan
Author: M.F. Shen

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