Second-order analysis of regret for sequential estimation of the autoregressive parameter in a first-order autoregressive model

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
T. N. Sriram, S. Samadi
{"title":"Second-order analysis of regret for sequential estimation of the autoregressive parameter in a first-order autoregressive model","authors":"T. N. Sriram, S. Samadi","doi":"10.1080/07474946.2019.1648933","DOIUrl":null,"url":null,"abstract":"Abstract This article revisits the problem of sequential point estimation of the autogressive parameter in an autoregressive model of order 1, where the errors are independent and identically distributed with mean 0 and unknown variance . This problem was originally considered in Sriram (1988), where first-order efficiency properties and a second-order expansion for the expected value of a stopping rule were established. Here, we obtain an asymptotic expression for the so-called regret due to not knowing σ, as the cost of estimation error tends to infinity. Under suitable assumptions, our extensive analysis shows that all but one term in the regret are asymptotically bounded. If the errors have a bounded support, however, then the regret remains asymptotically bounded. Finally, we illustrate the performance of our sequential procedure and the associated regret for well-known blowfly data (Nicholson, 1950) and Internet traffic data using the residual bootstrap method for autoregressive models.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"411 - 435"},"PeriodicalIF":0.6000,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1648933","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sequential Analysis-Design Methods and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07474946.2019.1648933","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1

Abstract

Abstract This article revisits the problem of sequential point estimation of the autogressive parameter in an autoregressive model of order 1, where the errors are independent and identically distributed with mean 0 and unknown variance . This problem was originally considered in Sriram (1988), where first-order efficiency properties and a second-order expansion for the expected value of a stopping rule were established. Here, we obtain an asymptotic expression for the so-called regret due to not knowing σ, as the cost of estimation error tends to infinity. Under suitable assumptions, our extensive analysis shows that all but one term in the regret are asymptotically bounded. If the errors have a bounded support, however, then the regret remains asymptotically bounded. Finally, we illustrate the performance of our sequential procedure and the associated regret for well-known blowfly data (Nicholson, 1950) and Internet traffic data using the residual bootstrap method for autoregressive models.
一阶自回归模型中自回归参数序列估计的二阶后悔分析
摘要本文重新讨论了1阶自回归模型中自压缩参数的序列点估计问题,其中误差是独立的,并且与均值0和未知方差同分布。这个问题最初是在Sriram(1988)中考虑的,其中建立了停止规则的期望值的一阶效率性质和二阶展开。在这里,我们得到了由于不知道σ而导致的所谓遗憾的渐近表达式,因为估计误差的代价趋于无穷大。在适当的假设下,我们的广泛分析表明,遗憾中除了一个项外,所有项都是渐近有界的。然而,如果误差具有有界支持,那么遗憾仍然是渐近有界的。最后,我们使用自回归模型的残差自举方法,说明了我们的序列过程的性能以及著名的飞蝇数据(Nicholson,1950)和互联网流量数据的相关遗憾。
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
1.40
自引率
12.50%
发文量
20
期刊介绍: The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.
×
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