Gini Covariance Matrix and Its Affine Equivariant Version

• Activity Number: 174
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lauren Weatherall*+ and Xin Dang and Hailin Sang
• Companies: and University of Mississippi and University of Mississippi
• Keywords: Gini mean difference ; spatial rank ; affine equivariance ; M-estimator ; transformation-retransformation

Abstract

We propose a new covariance matrix called Gini covariance matrix (GCM), which serves as a multivariate generalization of Gini mean difference (GMD). The extension is natural and based on the covariance representation of GMD and the spatial rank function. We study properties of the Gini covariance matrix. We propose an affine equavariant version of GCM, which is obtained through the transformation-retransformation technique. Estimation of both version of GCM has been presented. Consistency and normality of estimators have been established. Finally, robustness, efficiency and computation issues are discussed and compared with sample covariance matrix, Tyler-M estimator and other scatter estimators.