How Many Ways Can We Spell Gini Index?

• Activity Number: 291
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Statistics Without Borders
• Author(s): Sudheesh Kumar Kattumannil*+
• Companies: Michigan State University
• Keywords: Gini index ; Gini covariance ; U-statistics ; time series ; Moving average

Abstract

The Gini index and its variant are widely used to measure the variability in the model. Search for simple reliable estimator of the Gini index has lead to numerous publications. Most of these papers focus on the bias and the standard error of the estimator of the Gini index. In this paper, we propose a simple estimator of Gini index based on U-statistics. Asymptotic properties of the estimator are studied. A simulation study shows that our estimator performs 'well' compared to other estimators in terms of bias and mean squared error. In same direction, we discuss the estimation of Gini covariance and Gini correlation. We also suggest a simple unique approach to find the asymptotic distribution of the estimators of different inequality measures and then bring several works in this direction in to our uniform framework. The method described here provides a tool to find the explicit formula for the variance of the estimators of Gini index. Finally, some applications in time series are addressed.