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Title: On Kendall's tau for order statistics Authors:  Sebastian Fuchs - University of Salzburg (Austria) [presenting]
Klaus D Schmidt - University of Mannheim (Germany)
Abstract: Using Kendall's tau of the corresponding copulas, we compare the dependence structure of a random vector $ (X_1,\dots,X_d) $ with identical univariate marginals and that of its order statistic $(X_{1:d},\dots,X_{d:d})$. Although the corresponding copulas are in general not comparable with respect to pointwise or concordance order, it turns out that the value of Kendall's tau of the copula for the order statistic is always at least as large as that of the copula for the random vector. In the case where the univariate marginals are not only identical but also independent, we further calculate Kendall's tau for $(X_{1:d},\dots,X_{k:d})$ with $2 \leq k \leq d$ and show that this value is identical with that for $(X_{d-k+1:d},\dots,X_{d:d})$.