Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function

Holger Drees and Xin Huang

Journal of Multivariate Analysis, 1998, vol. 64, issue 1, 25-47

Abstract: It is well known that a bivariate distribution belongs to the domain of attraction of an extreme value distribution G if and only if the marginals belong to the domain of attraction of the univariate marginal extreme value distributions and the dependence function converges to the stable tail dependence function of G. Hall and Welsh (1984,Ann. Statist.12, 1079-1084) and Drees (1997b,Ann. Statist., to appear) addressed the problem of finding optimal rates of convergence for estimators of the extreme value index of an univariate distribution. The present paper deals with the corresponding problem for the stable tail dependence function. First an upper bound on the rate of convergence for estimators of the stable tail dependence function is established. Then it is shown that this bound is sharp by proving that it is attained by the tail empirical dependence function. Finally, we determine the limit distribution of this estimator if the dependence function satisfies a certain second-order condition.

Keywords: asymptotic normality; bivariate extreme value distribution; domain of attraction; rate of convergence; stable tail dependence function; tail empirical dependence function (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (70)

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