Asymptotic mean and variance of Gini correlation for bivariate normal samples

Authors:
Weichao Xu;Y. S. Hung;Mahesan Niranjan;Minfen Shen
Affiliations:
Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong;Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong;School of Electronics and Computer Science, University of Southampton, Southampton, U.K.;Department of Electrical Engineering, Shantou University, Shantou, Guangdong, China
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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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.