A0588
Title: Bootstrap-based inference for bivariate heteroscedastic extremes with a changing tail copula
Authors: Yifan Hu - Fudan Univeristy (China) [presenting]
Abstract: A novel copula-based model is introduced for independent but non-identically distributed data with heteroscedastic extremes marginal and changing tail dependence structures. A unified framework is established for joint inference on marginal tail distributions and tail dependence structure. This is achieved by demonstrating the weak convergence of the bivariate sequential tail empirical process and its empirical bootstrap counterpart. The asymptotic properties of several estimators are further derived on the tail, including the quasi-tail copula, the integrated scedasis function, and the Hill estimator, by treating them as functionals of the bivariate sequential tail empirical process. This process-centric approach not only facilitates the development of bootstrap-based methods but also ensures the theoretical validity of the derived statistics. Based on the inference framework, bootstrap-based tests are proposed for three critical hypotheses: The equivalence of extreme value indices, the equivalence of scedasis functions, and non-changing tail dependence when marginal scedasis functions are identical. Extensive simulations validate the robustness and efficiency of the three bootstrap-based tests, thereby validating the practical applicability of the proposed methods.
