On the rate of convergence to asymptotic independence between order statistics under power normalization with extension to the generalized order statistics

Based on the notion of the associated copula for order statistics and some L ₁-distances, we derive a symmetric nonparametric measure of asymptotic dependence between the order statistics under power normalization. This nonparametric criterion of dependence is extended to the generalized, as well as the dual generalized, order statistics.