Box-Cox Transformations and Bias Reduction in Extreme Value Theory

IF 0.9 Q3 MATHEMATICS, APPLIED
Lígia Henriques-Rodrigues, M. Ivette Gomes
{"title":"Box-Cox Transformations and Bias Reduction in Extreme Value Theory","authors":"Lígia Henriques-Rodrigues,&nbsp;M. Ivette Gomes","doi":"10.1155/2022/3854763","DOIUrl":null,"url":null,"abstract":"<div>\n <p>The Box-Cox transformations are used to make the data more suitable for statistical analysis. We know from the literature that this transformation of the data can increase the rate of convergence of the tail of the distribution to the generalized extreme value distribution, and as a byproduct, the bias of the estimation procedure is reduced. The reduction of bias of the Hill estimator has been widely addressed in the literature of extreme value theory. Several techniques have been used to achieve such reduction of bias, either by removing the main component of the bias of the Hill estimator of the extreme value index (EVI) or by constructing new estimators based on generalized means or norms that generalize the Hill estimator. We are going to study the Box-Cox Hill estimator introduced by Teugels and Vanroelen, in 2004, proving the consistency and asymptotic normality of the estimator and addressing the choice and estimation of the power and shift parameters of the Box-Cox transformation for the EVI estimation. The performance of the estimators under study will be illustrated for finite samples through small-scale Monte Carlo simulation studies.</p>\n </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/3854763","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Mathematical Methods","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2022/3854763","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

The Box-Cox transformations are used to make the data more suitable for statistical analysis. We know from the literature that this transformation of the data can increase the rate of convergence of the tail of the distribution to the generalized extreme value distribution, and as a byproduct, the bias of the estimation procedure is reduced. The reduction of bias of the Hill estimator has been widely addressed in the literature of extreme value theory. Several techniques have been used to achieve such reduction of bias, either by removing the main component of the bias of the Hill estimator of the extreme value index (EVI) or by constructing new estimators based on generalized means or norms that generalize the Hill estimator. We are going to study the Box-Cox Hill estimator introduced by Teugels and Vanroelen, in 2004, proving the consistency and asymptotic normality of the estimator and addressing the choice and estimation of the power and shift parameters of the Box-Cox transformation for the EVI estimation. The performance of the estimators under study will be illustrated for finite samples through small-scale Monte Carlo simulation studies.

Abstract Image

极值理论中的Box-Cox变换和偏差减少
Box-Cox变换用于使数据更适合统计分析。从文献中我们知道,数据的这种变换可以提高分布尾部向广义极值分布的收敛速度,并且作为一个副产品,估计过程的偏差减小了。在极值理论的文献中,希尔估计量的偏置减小问题得到了广泛的研究。已经使用了几种技术来实现这种减少偏差,或者通过消除极值指数(EVI)的Hill估计量的偏差的主要成分,或者通过构建基于广义均值或规范的新估计量来推广Hill估计量。我们将研究Teugels和Vanroelen在2004年引入的Box-Cox Hill估计量,证明了该估计量的相合性和渐近正态性,并解决了EVI估计的Box-Cox变换的功率和移位参数的选择和估计。所研究的估计器的性能将通过小型蒙特卡罗模拟研究来说明有限样本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
2.20
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信