Journal of Official Statistics, Vol.24, No.4, 2008. pp. 541–555
A Note on the Asymptotic Equivalence of Jackknife and Linearization Variance Estimation for the Gini Coefficient
Yves G. Berger
Abstract:The Gini coefficient (Gini 1914) has proved valuable as a measure of income inequality.
In cross-sectional studies of the Gini coefficient, information about the accuracy of its estimates
is crucial. We show how to use jackknife and linearization to estimate the variance of the Gini
coefficient, allowing for the effect of the sampling design. The aim is to show the asymptotic
equivalence (or consistency) of the generalized jackknife estimator (Campbell 1980) and the
Taylor linearization estimator (Kovačević and Binder 1997) for the variance of the Gini
coefficient. A brief simulation study supports our findings.
Keywords:Inclusion probability, linearization, survey weight, sampling design
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