Minimum sample sizes for confidence intervals for Gini’s mean difference: a new approach for their determination

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Articolo

Rivista

STATISTICA & APPLICAZIONI

Sezione

Open Access

Titolo

Minimum sample sizes for confidence intervals for Gini’s mean difference: a new approach for their determination

Autori

Francesca Greselin, Walter Maffenini

Editore

Vita e Pensiero

Formato

Articolo |

Pdf

Online da

01-2007

Issn

1824-6672 (stampa) | 2283-6659 (digitale)

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Descrizione Commenti dei lettori

The sample mean difference Â is an unbiased estimator of Gini’s mean difference A. It is well known that Â 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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