Testing the tail-dependence based on the radial component
A test is proposed for testing the hypothesis \(H_0\) on the tail independence of bivariate random vector \((X,Y)\) components. \((X,Y)\) is assumed to belong to the domain of max-attraction of an extreme value distribution with reverse exponential margins. The test statistics is constructed by the application of the Neyman-Pearson approach to the limiting distribution \(F\) of \(X+Y\) conditioned on \(X+Y>C\) when \(C\to\infty\). (Note, that \(F(t)=t\) under \(H_0\) and \(F(t)=t^{1+\rho}\) under the alternative). Approximate maximum likelihood estimate for \(\rho\) is considered. The performance of the test is explored by simulations. An application to sea-waves data is presented.
bivariate generalized Pareto distribution
uniformly most powerful Neyman-Pearson test
scientific article; zbMATH DE number 5520586