Veranstaltungen
Veranstaltungen der Fakultät für Mathematik
Minimizer of Kendall's tau and Kendall's tau for the Order Statistic, als mathkol osanadyn
Termin
19.06.2018, 14.15 Uhr - 15.15 Uhr
Veranstaltungsort
SR 611
Abstract
For the most popular measures of concordance, like Kendalls tau, Spearmans rho and Ginis gamma, the maximum value is equal to 1 and is attained by the upper Fréchet-Hoeffding bound and, in the bivariate case, the minimum value is equal to −1 and is attained by the lower Fréchet-Hoeffding bound.
In this class, Kendalls tau is particular since its minimum value (which depends on the dimension $d \geq 2$) is known and is attained by several distinct copulas whenver $d \geq 3$.
In the present talk, we characterize the classes of all copulas which maximize or minimize the value of Kendalls tau. We first show that the upper Fréchet-Hoeffding bound is the only copula maximizing Kendalls tau.
We then provide a characterization of the collection of all copulas minimizing Kendalls tau and we show that this collection is a singleton if and only if $d=2$.
As a complementary result, we show that the order transform of any copula minimizing Kendalls tau, which is related to the order statistic of certain random vectors, minimizes Kendalls tau as well.
Vortragende(r)
Sebastian Fuchs
Herkunft der/des Vortragenden
TU Dortmund