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

Greselin, F., Maffenini, W. (2007). Minimum sample sizes for confidence intervals for gini's mean difference: A new approach for their determination. STATISTICA & APPLICAZIONI, 5(1), 103-122.

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

GRESELIN, FRANCESCA;MAFFENINI, WALTER
2007

Abstract

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
Articolo in rivista - Articolo scientifico
Gini's Mean Difference, asymptotic confidence interval, U-statistic, minimum sample size, heavy tails
English
2007
5
1
103
122
open
Greselin, F., Maffenini, W. (2007). Minimum sample sizes for confidence intervals for gini's mean difference: A new approach for their determination. STATISTICA & APPLICAZIONI, 5(1), 103-122.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/2920
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