We consider extreme value analysis for independent but nonidentically distributed observations. In particular, the observations do not share the same extreme value index. Assuming continuously changing extreme value indices, we provide a nonparametric estimate for the functional extreme value index. Besides estimating the extreme value index locally, we also provide a global estimator for the trend and its joint asymptotic theory. The asymptotic theory for the global estimator can be used for testing a prespecified parametric trend in the extreme value indices. In particular, it can be applied to test whether the extreme value index remains at a constant level across all observations.

Hill estimator, Local and global estimation, Peak over threshold, Stochastic integral
dx.doi.org/10.1080/01621459.2019.1705307, hdl.handle.net/1765/124587
American Statistical Association. Journal
Erasmus University Rotterdam

de Haan, L.F.M, & Zhou, C. (2020). Trends in Extreme Value Indices. American Statistical Association. Journal. doi:10.1080/01621459.2019.1705307