The sample mean difference  is an unbiased estimator of Gini’s mean difference A. It is well
known that  is asymptotically normally distributed (Hoeffding, 1948). In order to obtain confidence
intervals for A, Â must be standardized and hence its variance Var(Â) must be estimated. In
this paper we study the effective coverage of the confidence intervals for A, when using a specific
unbiased estimator ^ Var(Â) for the variance of Â, 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.
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