Yi He published in The Annals of Statistics

Abstract
We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the 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, we consider a heterogeneous scales model 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. We also present asymptotic normality results for the extreme quantile estimator. A simulation study shows the good finite-sample behavior of our limit theorems. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.

Article citation and access to full article:

John H.J. Einmahl and Yi He, Extreme Value Inference for Heterogeneous Power Law Data, The Annals of Statistics , Volume 51(3), June 2023, p. 1331-1356, doi.org/10.1214/23-AOS2294. 

About

Yi He is an assistant professor at the Amsterdam School of Economics, University of Amsterdam (UvA). He received his PhD from Tilburg University and worked at Monash University, Australia before joining the UvA. His research focuses on high-dimensional econometrics, financial econometrics, extreme value analysis and machine learning. His works have been published in JRSS-b, JBES and AoS. He is a Tinbergen Institute research fellow.