Bootstrap-based Inference for Bivariate Heteroscedastic Extremes with a Changing Tail Copula

Abstract: This paper introduces a copula-based model for independent but non-identically distributed data with heteroscedastic extremes marginal and changing tail dependence structures. We establish a unified framework for inference by proving the weak convergence of the bivariate sequential tail empirical process and its empirical bootstrap counterpart. We derive the asymptotic properties of several estimators on the tail, including the quasi-tail copula, integrated scedasis function, and Hill estimator, treating them as functionals of the bivariate sequential tail empirical process. This process-centric approach enables the development of bootstrap-based methods and ensures the theoretical validity of the derived statistics. As an application of our inference method, we propose bootstrap-based tests for the equivalence of extreme value indices, the equivalence of scedasis functions, and non-changing tail dependence when marginal scedasis functions are identical. Our simulations validate the robustness and efficiency of the bootstrap-based tests.