Minimum sample sizes for confidence intervals for gini's mean difference: A new approach for their determination

The sample mean difference Delta^ is an unbiased estimator of Gini's mean difference Delta. It is well known that Delta^ is asymptotically normally distributed (Hoeffding, 1948). In order to obtain confidence intervals for Delta, Delta^ must be standardized and hence its variance must be estimated. In this paper we study the effective coverage of the confidence intervals for Delta, when using a specific unbiased estimator for the variance of Delta^, in a non-parametric framework. The empirical determination of the minimum sample size required to reach a good approximation of the nominal coverage is analyzed through a new approach. The reported results show that this threshold is critically related to the asymmetry and the tail heaviness in the underlying distribution