Two Symmetric and Computationally Efficient Gini Correlations

• Activity Number: 289 - Recent Advances in Mathematical Statistics and Probability
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: IMS
• Author(s): Courtney Vanderford* and Xin Dang and Yongli Sang
• Companies: University of Mississippi and University of Mississippi and University of Louisiana at Lafayette
• Keywords: Asymptotic relative efficiency; Computationally efficient Gini correlation; Influence function; Robustness; Symmetric Gini correlation

Abstract

The Gini correlation is useful for measuring dependence among random variables with heavy-tailed distributions. It's based on the covariance between one variable and rank of the other. Hence for each pair of variables, there are two Gini correlations that are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al(2016) proposed a symmetric Gini correlation based on joint spatial rank with computation cost O(n^2) where n is sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with computation cost O(nlogn). Properties of these symmetric Gini correlations are explored, influence functions are used to study robustness and asymptotic behavior, asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric lognormal distribution. Simulation and real data application are used to demonstrate desirable performance of the symmetric Gini correlations. This work is then extended to include bivariate Pareto distributions due to their usefulness in modelling many nonnegative socio-economic issues.