{"title":"基于块最大值法的引导估计器","authors":"Axel Bücher, Torben Staud","doi":"arxiv-2409.05529","DOIUrl":null,"url":null,"abstract":"The block maxima method is a standard approach for analyzing the extremal\nbehavior of a potentially multivariate time series. It has recently been found\nthat the classical approach based on disjoint block maxima may be universally\nimproved by considering sliding block maxima instead. However, the asymptotic\nvariance formula for estimators based on sliding block maxima involves an\nintegral over the covariance of a certain family of multivariate extreme value\ndistributions, which makes its estimation, and inference in general, an\nintricate problem. As an alternative, one may rely on bootstrap approximations:\nwe show that naive block-bootstrap approaches from time series analysis are\ninconsistent even in i.i.d.\\ situations, and provide a consistent alternative\nbased on resampling circular block maxima. As a by-product, we show consistency\nof the classical resampling bootstrap for disjoint block maxima, and that\nestimators based on circular block maxima have the same asymptotic variance as\ntheir sliding block maxima counterparts. The finite sample properties are\nillustrated by Monte Carlo experiments, and the methods are demonstrated by a\ncase study of precipitation extremes.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bootstrapping Estimators based on the Block Maxima Method\",\"authors\":\"Axel Bücher, Torben Staud\",\"doi\":\"arxiv-2409.05529\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The block maxima method is a standard approach for analyzing the extremal\\nbehavior of a potentially multivariate time series. It has recently been found\\nthat the classical approach based on disjoint block maxima may be universally\\nimproved by considering sliding block maxima instead. However, the asymptotic\\nvariance formula for estimators based on sliding block maxima involves an\\nintegral over the covariance of a certain family of multivariate extreme value\\ndistributions, which makes its estimation, and inference in general, an\\nintricate problem. As an alternative, one may rely on bootstrap approximations:\\nwe show that naive block-bootstrap approaches from time series analysis are\\ninconsistent even in i.i.d.\\\\ situations, and provide a consistent alternative\\nbased on resampling circular block maxima. As a by-product, we show consistency\\nof the classical resampling bootstrap for disjoint block maxima, and that\\nestimators based on circular block maxima have the same asymptotic variance as\\ntheir sliding block maxima counterparts. The finite sample properties are\\nillustrated by Monte Carlo experiments, and the methods are demonstrated by a\\ncase study of precipitation extremes.\",\"PeriodicalId\":501379,\"journal\":{\"name\":\"arXiv - STAT - Statistics Theory\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - STAT - Statistics Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.05529\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - STAT - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05529","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bootstrapping Estimators based on the Block Maxima Method
The block maxima method is a standard approach for analyzing the extremal
behavior of a potentially multivariate time series. It has recently been found
that the classical approach based on disjoint block maxima may be universally
improved by considering sliding block maxima instead. However, the asymptotic
variance formula for estimators based on sliding block maxima involves an
integral over the covariance of a certain family of multivariate extreme value
distributions, which makes its estimation, and inference in general, an
intricate problem. As an alternative, one may rely on bootstrap approximations:
we show that naive block-bootstrap approaches from time series analysis are
inconsistent even in i.i.d.\ situations, and provide a consistent alternative
based on resampling circular block maxima. As a by-product, we show consistency
of the classical resampling bootstrap for disjoint block maxima, and that
estimators based on circular block maxima have the same asymptotic variance as
their sliding block maxima counterparts. The finite sample properties are
illustrated by Monte Carlo experiments, and the methods are demonstrated by a
case study of precipitation extremes.