On the efficiency of Gini’s mean difference

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dc.contributor.authorGerstenberger, Carina
dc.contributor.authorVogel, Daniel
dc.date.accessioned2015-04-23T12:56:44Z
dc.date.available2015-04-23T12:56:44Z
dc.date.issued2015
dc.description.abstractThe asymptotic relative efficiency of the mean deviation with respect to the standard deviation is 88% at the normal distribution. In his seminal 1960 paper A survey of sampling from contaminated distributions, J. W. Tukey points out that, if the normal distribution is contaminated by a small c-fraction of a normal distribution with three times the standard deviation, the mean deviation is more efficient than the standard deviation - already for c < 1%. In the present article, we examine the efficiency of Gini's mean difference (the mean of all pairwise distances). Our results may be summarized by saying Gini's mean difference combines the advantages of the mean deviation and the standard deviation. In particular, an analytic expression for the finite- sample variance of Gini's mean difference at the normal mixture model is derived by means of the residue theorem, which is then used to determine the contamination fraction in Tukey's 1:3 normal mixture distribution that renders Gini's mean difference and the standard deviation equally effcient. We further compute the in influence function of Gini's mean difference, and carry out extensive finite-sample simulations.en
dc.identifier.urihttp://hdl.handle.net/2003/34066
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-5568
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB 823;10/2015
dc.subjectinfluence functionen
dc.subjectstandard deviationen
dc.subjectQnen
dc.subjectrobustnessen
dc.subjectresidue theoremen
dc.subjectnormal mixture distributionen
dc.subjectmedian absolute deviationen
dc.subjectmean deviationen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleOn the efficiency of Gini’s mean differenceen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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