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Activity Number: 584 - Advances in Semi- and Nonparametric Statistical Analysis
Type: Contributed
Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #330668
Title: The Bootstrap in Extreme Value Theory
Author(s): Chen Zhou*
Companies: De Nederlandsche Bank
Keywords: tail quantile process; block maxima; peak-over-threshold
Abstract:

Statistical inference based on extreme value theory uses only large observations in a sample. The large observations are selected by either the peaks-over-threshold (POT) method or by the block maxima (BM) method. Asymptotic theories for most estimators based on these two methods are established using the tail quantile process of the POT or the quantile process of block maxima. However, the asymptotic variance obtained in such asymptotic theories, though mostly explicit, can be intricate. One example is the much used probability weighted moment (PWM) estimator in the block maxima setup.

This paper develops a bootstrap analogue of the well-known asymptotic expansion of the (tail) quantile process in extreme value theory. More specifically, we derive a bootstrap version of the fundamental expansions for the (tail) quantile process in both the POT and BM setups.

Consequently, for any statistical estimator in extreme value theory whose asymptotic property is established via the (tail) quantile process, the bootstrap mimics faithfully the original asymptotic behavior of the estimator.


Authors who are presenting talks have a * after their name.

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