l估计量的唯一性结果,及其在l矩上的应用

Q Mathematics Statistical Methodology Pub Date : 2015-05-01 DOI:10.1016/j.stamet.2014.08.002
J.R.M. Hosking , N. Balakrishnan
{"title":"l估计量的唯一性结果,及其在l矩上的应用","authors":"J.R.M. Hosking ,&nbsp;N. Balakrishnan","doi":"10.1016/j.stamet.2014.08.002","DOIUrl":null,"url":null,"abstract":"<div><p><span>We show that if a linear combination<span> of expectations of order statistics has mean zero across all random variables that have finite mean, then the linear combination is identically zero. A consequence of this result is that any functional of a probability distribution can have essentially only one unbiased </span></span><span><math><mi>L</mi></math></span>-estimator (i.e., an estimator that has the form of a linear combination of order statistics): if two such linear combinations have the same expectation then they must be algebraically identical. We use this result to prove the equivalence of two statistics that have been proposed as estimators of the <em>L</em>-moments introduced by Hosking (1990), and to provide alternative means of computing estimators of the trimmed <em>L</em>-moments introduced by Elamir and Seheult (2003). We also make comparisons of the speed of various methods for computing estimators of <em>L</em>-moments and trimmed <em>L</em>-moments.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.08.002","citationCount":"8","resultStr":"{\"title\":\"A uniqueness result for L-estimators, with applications to L-moments\",\"authors\":\"J.R.M. Hosking ,&nbsp;N. Balakrishnan\",\"doi\":\"10.1016/j.stamet.2014.08.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>We show that if a linear combination<span> of expectations of order statistics has mean zero across all random variables that have finite mean, then the linear combination is identically zero. A consequence of this result is that any functional of a probability distribution can have essentially only one unbiased </span></span><span><math><mi>L</mi></math></span>-estimator (i.e., an estimator that has the form of a linear combination of order statistics): if two such linear combinations have the same expectation then they must be algebraically identical. We use this result to prove the equivalence of two statistics that have been proposed as estimators of the <em>L</em>-moments introduced by Hosking (1990), and to provide alternative means of computing estimators of the trimmed <em>L</em>-moments introduced by Elamir and Seheult (2003). We also make comparisons of the speed of various methods for computing estimators of <em>L</em>-moments and trimmed <em>L</em>-moments.</p></div>\",\"PeriodicalId\":48877,\"journal\":{\"name\":\"Statistical Methodology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.stamet.2014.08.002\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistical Methodology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1572312714000598\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312714000598","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 8

摘要

我们证明,如果有序统计量期望的线性组合在所有具有有限均值的随机变量上的平均值为零,则该线性组合等于零。这个结果的一个推论是,概率分布的任何泛函本质上只能有一个无偏l估计量(即,一个具有有序统计量线性组合形式的估计量):如果两个这样的线性组合具有相同的期望,那么它们必须在代数上相同。我们利用这一结果证明了霍斯金(1990)引入的l -矩估计量的两个统计量的等价性,并提供了计算Elamir和Seheult(2003)引入的修整l -矩估计量的替代方法。我们还比较了计算l -矩估计量和裁剪l -矩估计量的各种方法的速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
A uniqueness result for L-estimators, with applications to L-moments

We show that if a linear combination of expectations of order statistics has mean zero across all random variables that have finite mean, then the linear combination is identically zero. A consequence of this result is that any functional of a probability distribution can have essentially only one unbiased L-estimator (i.e., an estimator that has the form of a linear combination of order statistics): if two such linear combinations have the same expectation then they must be algebraically identical. We use this result to prove the equivalence of two statistics that have been proposed as estimators of the L-moments introduced by Hosking (1990), and to provide alternative means of computing estimators of the trimmed L-moments introduced by Elamir and Seheult (2003). We also make comparisons of the speed of various methods for computing estimators of L-moments and trimmed L-moments.

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
Statistical Methodology
Statistical Methodology STATISTICS & PROBABILITY-
CiteScore
0.59
自引率
0.00%
发文量
0
期刊介绍: Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.
期刊最新文献
Editorial Board Nonparametric M-estimation for right censored regression model with stationary ergodic data Symmetric directional false discovery rate control Estimation and goodness-of-fit in latent trait models: A comparison among theoretical approaches Some new results on the Rényi quantile entropy Ordering
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1