Confidence bounds for the true discovery proportion based on the exact distribution of the number of rejections

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Friederike Preusse, Anna Vesely, Thorsten Dickhaus
{"title":"Confidence bounds for the true discovery proportion based on the exact distribution of the number of rejections","authors":"Friederike Preusse,&nbsp;Anna Vesely,&nbsp;Thorsten Dickhaus","doi":"10.1007/s10463-024-00920-x","DOIUrl":null,"url":null,"abstract":"<div><p>In multiple hypotheses testing it has become widely popular to make inference on the true discovery proportion (TDP) of a set <span>\\(\\mathscr {M}\\)</span> of null hypotheses. This approach is useful for several application fields, such as neuroimaging and genomics. Several procedures to compute simultaneous lower confidence bounds for the TDP have been suggested in prior literature. Simultaneity allows for post-hoc selection of <span>\\(\\mathscr {M}\\)</span>. If sets of interest are specified a priori, it is possible to gain power by removing the simultaneity requirement. We present an approach to compute lower confidence bounds for the TDP if the set of null hypotheses is defined a priori. The proposed method determines the bounds using the exact distribution of the number of rejections based on a step-up multiple testing procedure under independence assumptions. We assess robustness properties of our procedure and apply it to real data from the field of functional magnetic resonance imaging.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 2","pages":"191 - 216"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the Institute of Statistical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10463-024-00920-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

Abstract

In multiple hypotheses testing it has become widely popular to make inference on the true discovery proportion (TDP) of a set \(\mathscr {M}\) of null hypotheses. This approach is useful for several application fields, such as neuroimaging and genomics. Several procedures to compute simultaneous lower confidence bounds for the TDP have been suggested in prior literature. Simultaneity allows for post-hoc selection of \(\mathscr {M}\). If sets of interest are specified a priori, it is possible to gain power by removing the simultaneity requirement. We present an approach to compute lower confidence bounds for the TDP if the set of null hypotheses is defined a priori. The proposed method determines the bounds using the exact distribution of the number of rejections based on a step-up multiple testing procedure under independence assumptions. We assess robustness properties of our procedure and apply it to real data from the field of functional magnetic resonance imaging.

真实发现比例的置信限基于拒绝数量的精确分布
在多假设检验中,对一组\(\mathscr {M}\)零假设的真发现比例(TDP)进行推断已成为一种广泛流行的方法。这种方法在神经成像和基因组学等多个应用领域都很有用。在以前的文献中提出了几种计算TDP同时较低置信界限的方法。同时性允许事后选择\(\mathscr {M}\)。如果感兴趣的集合是先验地指定的,则有可能通过去除同时性要求来获得权力。我们提出了一种方法来计算低置信界限的TDP,如果零假设的集合是先验定义的。该方法在独立假设条件下,基于升压多重检验过程,利用拒绝数的精确分布确定边界。我们评估我们程序的鲁棒性,并将其应用于功能磁共振成像领域的实际数据。
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
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
×
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