总体分位数平滑贝叶斯Bootstrap区间的高阶覆盖

IF 0.6 Q4 STATISTICS & PROBABILITY

Austrian Journal of Statistics Pub Date : 2023-03-12 DOI:10.17713/ajs.v52i2.1385

David M. Kaplan, Lonnie Hofmann

{"title":"总体分位数平滑贝叶斯Bootstrap区间的高阶覆盖","authors":"David M. Kaplan, Lonnie Hofmann","doi":"10.17713/ajs.v52i2.1385","DOIUrl":null,"url":null,"abstract":"We characterize the high-order coverage accuracy of smoothed and unsmoothed Bayesian bootstrap confidence intervals for population quantiles. Although the original (Rubin 1981) unsmoothed intervals have the same O(n−1/2) coverage error as the standard empirical bootstrap, the smoothed Bayesian bootstrap of Banks (1988) has much smaller O(n−3/2[log(n)]3) coverage error and is exact in special cases, without requiring any smoothing parameter. It automatically removes an error term of order 1/n that other approaches need to explicitly correct for. This motivates further study of the smoothed Bayesian bootstrap in more complex settings and models.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"25 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"High-order Coverage of Smoothed Bayesian Bootstrap Intervals for Population Quantiles\",\"authors\":\"David M. Kaplan, Lonnie Hofmann\",\"doi\":\"10.17713/ajs.v52i2.1385\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We characterize the high-order coverage accuracy of smoothed and unsmoothed Bayesian bootstrap confidence intervals for population quantiles. Although the original (Rubin 1981) unsmoothed intervals have the same O(n−1/2) coverage error as the standard empirical bootstrap, the smoothed Bayesian bootstrap of Banks (1988) has much smaller O(n−3/2[log(n)]3) coverage error and is exact in special cases, without requiring any smoothing parameter. It automatically removes an error term of order 1/n that other approaches need to explicitly correct for. This motivates further study of the smoothed Bayesian bootstrap in more complex settings and models.\",\"PeriodicalId\":51761,\"journal\":{\"name\":\"Austrian Journal of Statistics\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Austrian Journal of Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17713/ajs.v52i2.1385\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Austrian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17713/ajs.v52i2.1385","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

我们描述了总体分位数的平滑和非平滑贝叶斯自举置信区间的高阶覆盖精度。尽管原始(Rubin 1981)的非平滑区间与标准经验bootstrap具有相同的O(n−1/2)覆盖误差，但Banks(1988)的平滑贝叶斯bootstrap具有更小的O(n−3/2[log(n)]3)覆盖误差，并且在特殊情况下是精确的，不需要任何平滑参数。它会自动去除1/n阶的错误项，而其他方法需要显式纠正。这激发了在更复杂的设置和模型中进一步研究平滑贝叶斯自举。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

High-order Coverage of Smoothed Bayesian Bootstrap Intervals for Population Quantiles

We characterize the high-order coverage accuracy of smoothed and unsmoothed Bayesian bootstrap confidence intervals for population quantiles. Although the original (Rubin 1981) unsmoothed intervals have the same O(n−1/2) coverage error as the standard empirical bootstrap, the smoothed Bayesian bootstrap of Banks (1988) has much smaller O(n−3/2[log(n)]3) coverage error and is exact in special cases, without requiring any smoothing parameter. It automatically removes an error term of order 1/n that other approaches need to explicitly correct for. This motivates further study of the smoothed Bayesian bootstrap in more complex settings and models.

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

Austrian Journal of Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 weeks

期刊介绍： The Austrian Journal of Statistics is an open-access journal (without any fees) with a long history and is published approximately quarterly by the Austrian Statistical Society. Its general objective is to promote and extend the use of statistical methods in all kind of theoretical and applied disciplines. The Austrian Journal of Statistics is indexed in many data bases, such as Scopus (by Elsevier), Web of Science - ESCI by Clarivate Analytics (formely Thompson & Reuters), DOAJ, Scimago, and many more. The current estimated impact factor (via Publish or Perish) is 0.775, see HERE, or even more indices HERE. Austrian Journal of Statistics ISNN number is 1026597X Original papers and review articles in English will be published in the Austrian Journal of Statistics if judged consistently with these general aims. All papers will be refereed. Special topics sections will appear from time to time. Each section will have as a theme a specialized area of statistical application, theory, or methodology. Technical notes or problems for considerations under Shorter Communications are also invited. A special section is reserved for book reviews.