Bootstrapping Extreme Value Estimators

This article develops a bootstrap analogue of the well-known asymptotic expansion of the tail quantile process in extreme value theory. One application of this result is to construct confidence intervals for estimators of the extreme value index such as the Probability Weighted Moment (PWM) estimato...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2024-01, Vol.119 (545), p.382-393
Main Authors: de Haan, Laurens, Zhou, Chen
Format: Article
Language:English
Subjects:
Asymptotic series
Block maxima
Bootstrap method
Confidence intervals
Consistency
Estimators
Extreme value theory
Extreme values
Peak-over-threshold
Quantiles
Statistical analysis
Statistics
Tail quantile process
Variance
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Summary:This article develops a bootstrap analogue of the well-known asymptotic expansion of the tail quantile process in extreme value theory. One application of this result is to construct confidence intervals for estimators of the extreme value index such as the Probability Weighted Moment (PWM) estimator. For the peaks-over-threshold method, we show the bootstrap consistency of the confidence intervals. By contrast, the asymptotic expansion of the quantile process of the bootstrapped block maxima does not lead to a similar consistency result for the PWM estimator using the block maxima method. For both methods, We show by simulations that the sample variance of bootstrapped estimates can be a good approximation for the asymptotic variance of the original estimator. Supplementary materials for this article are available online.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2022.2120400