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

Name: Minimum sample sizes for confidence intervals for Gini’s mean difference: a new approach for their determination
Brand: Vita e Pensiero
Availability: OnlineOnly

digital

Article

Magazine

STATISTICA & APPLICAZIONI

Section

Open Access

Title

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

Authors

Francesca Greselin, Walter Maffenini

Publisher

Vita e Pensiero

Format

Article |

Pdf

Pages

Online from

01-2007

Issn

1824-6672 (print) | 2283-6659 (digital)

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Description Readers' comments

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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