Performance comparison of estimators based on different norms of bivariate regular variation

This paper investigates the performance discrepancy among estimators based on different norms of elliptical bivariate regular variation.Bivariate regular variation is specified by tail index and spectral measure that has a parametric form for the elliptical type.Note that the parametric form depends on the norm.Therefore, since the resulting likelihood function also varies along with norm, we can derive different estimators.Comparing 3 estimators based on L 1 , L 2 , and maximum norms, respectively, it turns out that they have different accuracies.However, there is no universal superior one among them.Meanwhile, the standard error is a promising indicator of performance and can be utilized to select the most suitable one of the estimators under consideration for analyzing the data at hand.For demonstration, we apply the proposed estimators for the standardized residuals of real bivariate return series and conclude that the maximum norm based estimator is the most suitable.