Hill估计量的归一化变换

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Australian & New Zealand Journal of Statistics Pub Date : 2025-07-10 DOI:10.1111/anzs.70016

Rikako Nomura, Yan Liu

{"title":"Hill估计量的归一化变换","authors":"Rikako Nomura, Yan Liu","doi":"10.1111/anzs.70016","DOIUrl":null,"url":null,"abstract":"<p>We present a normalising transformation of the Hill estimator to improve the convergence rate in finite-sample performance. Our proposal for the normalising transformation is based on the higher order asymptotic expansion of the Hill estimator. The transformation is automatic and simple in computation. The resulting transformation theoretically improves the approximation to the standard normal distribution, achieving a lower error rate compared with the variance stabilisation or the Wilson and Hilferty approximation. The numerical results of simulations also align with our theoretical findings.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 3","pages":"367-372"},"PeriodicalIF":0.8000,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70016","citationCount":"0","resultStr":"{\"title\":\"Normalising Transformation of the Hill Estimator\",\"authors\":\"Rikako Nomura, Yan Liu\",\"doi\":\"10.1111/anzs.70016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We present a normalising transformation of the Hill estimator to improve the convergence rate in finite-sample performance. Our proposal for the normalising transformation is based on the higher order asymptotic expansion of the Hill estimator. The transformation is automatic and simple in computation. The resulting transformation theoretically improves the approximation to the standard normal distribution, achieving a lower error rate compared with the variance stabilisation or the Wilson and Hilferty approximation. The numerical results of simulations also align with our theoretical findings.</p>\",\"PeriodicalId\":55428,\"journal\":{\"name\":\"Australian & New Zealand Journal of Statistics\",\"volume\":\"67 3\",\"pages\":\"367-372\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70016\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Australian & New Zealand Journal of Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/anzs.70016\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Australian & New Zealand Journal of Statistics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/anzs.70016","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

为了提高有限样本性能的收敛速度，我们提出了Hill估计量的一种归一化变换。我们提出了基于Hill估计量的高阶渐近展开的归一化变换。该变换是自动的，计算简单。由此产生的变换在理论上改善了对标准正态分布的近似，与方差稳定或Wilson和Hilferty近似相比，实现了更低的错误率。模拟的数值结果也与我们的理论发现一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Normalising Transformation of the Hill Estimator

查看原文本刊更多论文

Normalising Transformation of the Hill Estimator

We present a normalising transformation of the Hill estimator to improve the convergence rate in finite-sample performance. Our proposal for the normalising transformation is based on the higher order asymptotic expansion of the Hill estimator. The transformation is automatic and simple in computation. The resulting transformation theoretically improves the approximation to the standard normal distribution, achieving a lower error rate compared with the variance stabilisation or the Wilson and Hilferty approximation. The numerical results of simulations also align with our theoretical findings.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Australian & New Zealand Journal of Statistics 数学-统计学与概率论

CiteScore

1.30

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.