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May 2021 Asymptotics for sliding blocks estimators of rare events
Holger Drees, Sebastian Neblung
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Bernoulli 27(2): 1239-1269 (May 2021). DOI: 10.3150/20-BEJ1272

Abstract

Drees and Rootzén (Ann. Statist. 38 (2010) 2145–2186) have established limit theorems for a general class of empirical processes of statistics that are useful for the extreme value analysis of time series, but do not apply to statistics of sliding blocks, including so-called runs estimators. We generalize these results to empirical processes which cover both the class considered by Drees and Rootzén (Ann. Statist. 38 (2010) 2145–2186) and processes of sliding blocks statistics. Using this approach, one can analyze different types of statistics in a unified framework. We show that statistics based on sliding blocks are asymptotically normal with an asymptotic variance which, under rather mild conditions, is smaller than or equal to the asymptotic variance of the corresponding estimator based on disjoint blocks. Finally, the general theory is applied to three well-known estimators of the extremal index. It turns out that they all have the same limit distribution, a fact which has so far been overlooked in the literature.

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Holger Drees. Sebastian Neblung. "Asymptotics for sliding blocks estimators of rare events." Bernoulli 27 (2) 1239 - 1269, May 2021. https://doi.org/10.3150/20-BEJ1272

Information

Received: 1 April 2020; Revised: 1 September 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1272

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 2 • May 2021
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