Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

L. Barmoodeh, M. Naghizadeh Qomi
{"title":"Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations","authors":"L. Barmoodeh, M. Naghizadeh Qomi","doi":"10.51936/uivd4115","DOIUrl":null,"url":null,"abstract":"Considering a Pareto model with unknown shape and scale parameters \\(\\alpha\\) and \\(\\beta\\), respectively, we are interested in Thompson shrinkage test estimation for the shape parameter \\(\\alpha\\) under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for \\(\\alpha\\) and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for \\(\\alpha\\) with the help of a point guess value \\(\\alpha_0\\) and record observations. We investigate the risk-bias of these estimators and compute their risks numerically. A comparison is performed between the PTS estimators and a risk-unbiased estimator. A numerical example is presented for illustrative and comparative purposes. We end the paper by discussion and concluding remarks.","PeriodicalId":242585,"journal":{"name":"Advances in Methodology and Statistics","volume":"75 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Methodology and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.51936/uivd4115","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

Considering a Pareto model with unknown shape and scale parameters \(\alpha\) and \(\beta\), respectively, we are interested in Thompson shrinkage test estimation for the shape parameter \(\alpha\) under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for \(\alpha\) and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for \(\alpha\) with the help of a point guess value \(\alpha_0\) and record observations. We investigate the risk-bias of these estimators and compute their risks numerically. A comparison is performed between the PTS estimators and a risk-unbiased estimator. A numerical example is presented for illustrative and comparative purposes. We end the paper by discussion and concluding remarks.
预测试收缩估计的形状参数的帕累托模型使用先验点知识和记录的观察
考虑一个形状和尺度参数分别为\(\alpha\)和\(\beta\)未知的Pareto模型,我们对形状参数\(\alpha\)在平方对数误差损失(SLEL)函数下的汤普森收缩试验估计感兴趣。我们找到了\(\alpha\)的一个风险无偏估计量,并计算了它在SLEL下的风险。根据Thompson(1986),我们借助点猜测值\(\alpha_0\)和记录观测值构建\(\alpha\)的预试收缩(PTS)估计器。我们研究了这些估计器的风险偏差,并用数值方法计算了它们的风险。在PTS估计量和风险无偏估计量之间进行比较。为了说明和比较,给出了一个数值例子。我们以讨论和结束语结束本文。
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
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:604180095
Book学术官方微信