Michigan State University A CLASS OF ESTIMATORS: A UNIFYING TOOL TOWARDS THE ESTIMATION OF GINI INDEX AND ITS VARIANT

Abstract. The Gini index and its variant are widely used as a mea-sure of income inequality. Finding reliable estimators of these measures and studying its asymptotic properties has been an important area of research in the last two decades. Due to the fragmentation of literature among statistician and economist, several results in this direction have been republished often with a clear lack of reference to previous work. In this paper, we propose a simple unique approach to find the estimators of different income inequality measures. Asymptotic properties of these estimators can be proved in an identical way. The method described here provides an explicit formula for finding the asymptotic variance of the proposed estimators. A consistent estimator of the asymptotic variance can also find by plug-in method. We bring several research problems related to the estimation of Gini index and related concepts into our uniform framework. The asymptotic distribution obtained for Gini co-variance has far reaching consequence due to its potential application in non-linear time series analysis