Asymptotic confidence intervals for a new inequality measure

Recently Zenga (2007) introduced a new inequality measure based on ratios between lower and upper group means. Differently from Gini's index, which may be expressed as a ratio of two regular functionals (Hoeffding, 1948), the new index is defined as a mean of several ratios and classical U-statistics theory does not seem to apply directly. In this paper the performance of asymptotic confidence intervals for Gini's measure and for the new measure is tested. Several types of confidence intervals are considered: the normal, the percentile, the BCa and the t-bootstrap. While the underlying asymptotic theory for Gini's measure is well established, formal proofs for Zenga's index are still missing in literature. Nevertheless, also in view of our simulation results, asymptotic properties similar to those of Gini's index can be expected to hold also for Zenga's new inequality measure.