The study of the Gini concentration ratio by means of the influence function

Abstract

In this paper the influence function of the Gini concentration ratio is determined. The resulting function is used to verify the robustness properties of the functional, which proves sensitive to the presence of outliers. The local shift sensitivity is then determined and it is shown to be bounded under the assumption that income is a continuous random variable. Finally the influence function is used in the approximation of the bias of Gini's concentration ratio due to grouped data.