Trends in Extreme Value Indices

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.

Automated summary

This study explores extreme value analysis for independent but nonidentically distributed observations, providing a nonparametric estimate for the functional extreme value index. In addition to locally estimating the extreme value index, a global estimator for the trend and its joint asymptotic theory are also offered for testing a prespecified parametric trend in the extreme value indices. It can be applied to test whether the extreme value index remains at a constant level across all observations.