About the accuracy of estimates of maximum likelihood in bivariate distributions of extreme values

The non-degenerated limit distributions of normalized maxima are the so called bivariate extreme value distributions. When modeling the asymptotic probabilistic behavior of extremes the objective is to obtain good approximations for the bivariate extremes distributions allowing the investigation of simultaneous extreme events. Typically the sample sizes are small, and this raises questions related to the quality and accuracy of the maximum likelihood estimates of the parameters and other quantities derived from the models. In this article we use bootstrap resampling schemes and Monte Carlo simulations to assess the variability and to construct confidence intervals for these estimates, in order to establish how reliable are the conclusions drawn from the analyses based on these models. Critical values for the tests proposed in Tawn are obtained through simulations.