Regular score tests of independence in multivariate extreme values (Q2488468)

Score tests for independence based on i.i.d. bivariate observations are considered under the assumption that their common CDF is \( F(x,y)=\exp\{-(x^{-1/\alpha}+y^{-1/\alpha})^\alpha\} \) with \((x,y)\) in a specified region, e.g., for \(x>u\) and \(y>u\), where \(u\) is a high threshold. The independence corresponds to \(\alpha=1\). In the regularized score test, the observations exceeding a high level are censored and only the information of their number is used in the likelihood. This is done to derive a test statistics with finite variance. The approximated p-levels of the tests are calculated basing on the asymptotic normality of the obtained statistics. Statistical properties of these tests and Kendall's \(\tau\)-based test are compared via simulations.