caa a22 4500 60619651X CHVBK 20210128100924.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s10260-015-0315-x doi (NATIONALLICENCE)springer-10.1007/s10260-015-0315-x On the efficiency of Gini's mean difference [Elektronische Daten] [Carina Gerstenberger, Daniel Vogel] The 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 $$\epsilon $$ ϵ -fraction of a normal distribution with three times the standard deviation, the mean deviation is more efficient than the standard deviation—already for $$\epsilon < 1\,\%$$ ϵ < 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 efficient. We further compute the influence function of Gini's mean difference, and carry out extensive finite-sample simulations. Springer-Verlag Berlin Heidelberg, 2015 Influence function nationallicence Mean deviation nationallicence Median absolute deviation nationallicence Normal mixture distribution nationallicence Residue theorem nationallicence Robustness nationallicence $$Q_n$$ Q n nationallicence Standard deviation nationallicence Gerstenberger Carina Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut Vogel Daniel Institute for Complex Systems and Mathematical Biology, University of Aberdeen, AB24 3UE, Aberdeen, UK aut Statistical Methods & Applications Springer Berlin Heidelberg 24/4(2015-11-01), 569-596 1618-2510 24:4<569 2015 24 10260 https://doi.org/10.1007/s10260-015-0315-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10260-015-0315-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gerstenberger Carina Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut NATIONALLICENCE 700 1- Vogel Daniel Institute for Complex Systems and Mathematical Biology, University of Aberdeen, AB24 3UE, Aberdeen, UK aut NATIONALLICENCE 773 0- Statistical Methods & Applications Springer Berlin Heidelberg 24/4(2015-11-01), 569-596 1618-2510 24:4<569 2015 24 10260