文章基本信息

标题：The variance of Gini’s mean difference and its estimators
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作者：Michele Zenga ; Marcella Polisicchio ; Francesca Greselin 等
期刊名称：Statistica
印刷版ISSN：1973-2201
出版年度：2004
卷号：64
期号：3
页码：455-475
DOI：10.6092/issn.1973-2201/50
语种：English
出版社：Dep. of Statistical Sciences "Paolo Fortunati", Università di Bologna
摘要：The use of Gini’s mean difference as an index of variability has, until now, been restricted because of some difficulties arising in computing and estimating the variance of its estimator d. The aim of this paper is to cope with these issues. Considering the mean deviation D(x) of a r.v. X about a given value x, the Gini’s mean difference d results to be the expected value of D(x). Moreover, denoting by f the expected value of D2(x) and by d the sample mean difference without repetition, Var(d) can be expressed as a function of the variance of X, say s2, d and f. Two estimators for Var(d) are obtained: starting from the natural estimator, whose asympthotic unbiasedness is shown, an unbiased estimator is then derived.