Shrinkage estimation of Gini index

The Gini index is an indicator of the degree of income inequality in a society. In recent decades, the Gini index has become a popular means of describing the inequality measure. In this article, we propose shrinkage estimation strategies for estimating the Gini indices for multiple populations. The classical estimator is investigated as a competitor of the proposed estimators. In light of a quadratic loss function, the asymptotic risks of the estimators are derived. A central theme of this paper is that the shrinkage method provides a powerful extension of its classical counterpart for the estimation of Gini indices in a multi-population situation.