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Activity Number: 71
Type: Contributed
Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract #315759
Title: Symmetric Gini Covariance and Correlation
Author(s): Yongli Sang*
Companies:
Keywords: Gini's mean difference ; Gini correlation ; Robustness ; Efficiency
Abstract:

Gini covariance as a measure of dependence between two variables plays an important role in Gini methodology. In this paper, we propose a new symmetric Gini-type covariance based on a joint rank function. As a result, a new correlation called the symmetrical Gini correlation (Gcor, $\rho_g$) is also defined. We study the properties of Gcor. Its influence function is derived and shows that it is more robust than Pearson correlation but less robust than Kendall $\tau$. The relation between the symmetric Gini correlation $\rho_g$ and the linear correlation $\rho$ is established for a class of random vectors in the family of elliptical distributions. With this relationship, an estimator of $\rho$ is obtained from estimating $\rho_g$. We study the asymptotic normality of this estimator through two approaches: one from influence function and the other from U-statistics and Delta method. We compare asymptotic efficiencies of linear correlation estimators based on Gini, Pearson and Kendall $\tau$ under various distributions.The proposed one not only balances between robustness and efficiency, its superior finite sample behavior also makes it advantageous in application.


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