Bootstrapping Extreme Value Estimators

• 成果类型: Article
• 署名作者: de Haan, Laurens; Zhou, Chen
• 署名单位: Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC; Universidade de Lisboa; Tinbergen Institute
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2120400
• 发表日期: 2024
• 页码: 382-393
• 关键词: parameter

摘要

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.