非均质样本上有限假设数的多重假设检验问题中错误概率之和的双侧估计值

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2024-08-14 DOI:10.1137/s0040585x97t991945

M. P. Savelov

{"title":"非均质样本上有限假设数的多重假设检验问题中错误概率之和的双侧估计值","authors":"M. P. Savelov","doi":"10.1137/s0040585x97t991945","DOIUrl":null,"url":null,"abstract":"Theory of Probability &Its Applications, Volume 69, Issue 2, Page 322-330, August 2024. <br/> We obtain two-sided estimates for the weighted sum of probabilities of errors in the multiple hypothesis testing problem with finite number of hypotheses on a nonhomogeneous sample of size $n$. The obtained upper and lower estimates are shown to converge to zero exponentially fast with increasing $n$ in a wide class of cases. The results obtained can be used for deriving two-sided estimates for the size of a sample required for multiple hypothesis testing.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"32 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two-sided Estimates for the Sum of Probabilities of Errors in the Multiple Hypothesis Testing Problem with Finite Number of Hypotheses on a Nonhomogeneous Sample\",\"authors\":\"M. P. Savelov\",\"doi\":\"10.1137/s0040585x97t991945\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Theory of Probability &Its Applications, Volume 69, Issue 2, Page 322-330, August 2024. <br/> We obtain two-sided estimates for the weighted sum of probabilities of errors in the multiple hypothesis testing problem with finite number of hypotheses on a nonhomogeneous sample of size $n$. The obtained upper and lower estimates are shown to converge to zero exponentially fast with increasing $n$ in a wide class of cases. The results obtained can be used for deriving two-sided estimates for the size of a sample required for multiple hypothesis testing.\",\"PeriodicalId\":51193,\"journal\":{\"name\":\"Theory of Probability and its Applications\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/s0040585x97t991945\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991945","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: 0

摘要

概率论及其应用》（Theory of Probability &Its Applications），第 69 卷第 2 期，第 322-330 页，2024 年 8 月。我们获得了大小为 $n$ 的非均质样本上有限个假设的多重假设检验问题中错误概率加权和的双侧估计值。结果表明，在很多情况下，随着 $n$ 的增大，所得到的上估计值和下估计值会以指数级的速度趋近于零。所得结果可用于推导多重假设检验所需的样本大小的双侧估计值。

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

Two-sided Estimates for the Sum of Probabilities of Errors in the Multiple Hypothesis Testing Problem with Finite Number of Hypotheses on a Nonhomogeneous Sample

Theory of Probability &Its Applications, Volume 69, Issue 2, Page 322-330, August 2024.
We obtain two-sided estimates for the weighted sum of probabilities of errors in the multiple hypothesis testing problem with finite number of hypotheses on a nonhomogeneous sample of size $n$. The obtained upper and lower estimates are shown to converge to zero exponentially fast with increasing $n$ in a wide class of cases. The results obtained can be used for deriving two-sided estimates for the size of a sample required for multiple hypothesis testing.

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

Theory of Probability and its Applications 数学-统计学与概率论

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.