B0158
Title: Extreme value inference for heterogeneous data
Authors: John Einmahl - Tilburg University (Netherlands) [presenting]
Yi He - University of Amsterdam (Netherlands)
Abstract: Extreme value statistics are extended to independent data with possibly very different distributions. In particular, a novel asymptotic normality result is presented for the Hill estimator, which now estimates the positive extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, a heterogeneous scales model is considered where the asymptotic variance can be calculated explicitly. The primary tool for the proofs is the functional central limit theorem for a weighted tail empirical process. Asymptotic normality results are also presented for the extreme quantile estimator and an application to assessing more accurately the tail heaviness of earthquake energies. Finally, the general case is considered, where the extreme value index of the average distribution is real-valued, and a new asymptotic normality result is presented for the moment estimator.
