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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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Published in: | Journal of the American Statistical Association 2024-01, Vol.119 (545), p.382-393 |
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description | 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. |
doi_str_mv | 10.1080/01621459.2022.2120400 |
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Supplementary materials
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Supplementary materials
for this article are available online.</description><subject>Asymptotic series</subject><subject>Block maxima</subject><subject>Bootstrap method</subject><subject>Confidence intervals</subject><subject>Consistency</subject><subject>Estimators</subject><subject>Extreme value theory</subject><subject>Extreme values</subject><subject>Peak-over-threshold</subject><subject>Quantiles</subject><subject>Statistical analysis</subject><subject>Statistics</subject><subject>Tail quantile process</subject><subject>Variance</subject><issn>0162-1459</issn><issn>1537-274X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>0YH</sourceid><sourceid>8BJ</sourceid><recordid>eNp9kFtLAzEQhYMoWKs_QSgIvm2dXNYkb16oFyj4ouJbyGYT2bLdrJMU7b93l9ZX52Vg5jtnhkPIOYU5BQVXQK8ZFaWeM2BszigDAXBAJrTksmBSfBySycgUI3RMTlJawVBSqQm5vIsxp4y275vuc7b4yejXfvZu242fLVJu1jZHTKfkKNg2-bN9n5K3h8Xr_VOxfHl8vr9dFk5QlYtaOw91zUoXaBW0tlawSsE4liAqWlFttZfa8TpAcKUFLjlQK6wIlGnOp-Ri59tj_Nr4lM0qbrAbTpphLUuuQKuBKneUw5gS-mB6HB7FraFgxkjMXyRmjMTsIxl0Nztd04WIa_sdsa1Ntts2YkDbuSYZ_r_FLwWGZwI</recordid><startdate>20240102</startdate><enddate>20240102</enddate><creator>de Haan, Laurens</creator><creator>Zhou, Chen</creator><general>Taylor & Francis</general><general>Taylor & Francis Ltd</general><scope>0YH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope><scope>K9.</scope></search><sort><creationdate>20240102</creationdate><title>Bootstrapping Extreme Value Estimators</title><author>de Haan, Laurens ; Zhou, Chen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c418t-d9ce0dd25cf1bf99aa42b80d9ce704b1b19a9e79c3df0fc5a037301a4a4f12933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Asymptotic series</topic><topic>Block maxima</topic><topic>Bootstrap method</topic><topic>Confidence intervals</topic><topic>Consistency</topic><topic>Estimators</topic><topic>Extreme value theory</topic><topic>Extreme values</topic><topic>Peak-over-threshold</topic><topic>Quantiles</topic><topic>Statistical analysis</topic><topic>Statistics</topic><topic>Tail quantile process</topic><topic>Variance</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>de Haan, Laurens</creatorcontrib><creatorcontrib>Zhou, Chen</creatorcontrib><collection>Taylor & Francis Open Access(OpenAccess)</collection><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><jtitle>Journal of the American Statistical Association</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>de Haan, Laurens</au><au>Zhou, Chen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bootstrapping Extreme Value Estimators</atitle><jtitle>Journal of the American Statistical Association</jtitle><date>2024-01-02</date><risdate>2024</risdate><volume>119</volume><issue>545</issue><spage>382</spage><epage>393</epage><pages>382-393</pages><issn>0162-1459</issn><eissn>1537-274X</eissn><abstract>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
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source | International Bibliography of the Social Sciences (IBSS); Taylor and Francis Science and Technology Collection |
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 |
title | Bootstrapping Extreme Value Estimators |
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