Estimation of the coefficient of tail dependence in bivariate extremes
Suppose a bivariate random vector \((X,Y)\) is in the domain of attraction of an extreme value distribution. Under certain assumptions on the bivariate upper tail behavior of \((X,Y)\), \textit{A.W. Ledford} and \textit{J.A. Tawn} [Biometrika 83, No. 1, 169-187 (1996; Zbl 0865.62040)] introduced an index of tail dependence \(\eta\) and studied the asymptotic properties of its estimator proposed by them. Here, under a more restrictive assumption on the bivariate tail behavior that makes \(\eta < 1\) if and only if the component random variables are asymptotically (upper-tail) independent, a nonparametric estimator is proposed and is shown to be asymptotically normal. It is used to estimate \(P(X > x, Y > y)\) for large \(x, y\). This estimator is also used to test asymptotic independence for a data on storm events.
scientific article; zbMATH DE number 1395199