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Fundamental Limits in Large-Scale Multiple Testing and Its Application.
Fundamental Limits in Large-Scale Multiple Testing and Its Application.
상세정보
- 자료유형
- 학위논문
- Control Number
- 0017160442
- International Standard Book Number
- 9798383565728
- Dewey Decimal Classification Number
- 310
- Main Entry-Personal Name
- Nie, Yutong.
- Publication, Distribution, etc. (Imprint
- [S.l.] : Yale University., 2024
- Publication, Distribution, etc. (Imprint
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- Physical Description
- 114 p.
- General Note
- Source: Dissertations Abstracts International, Volume: 86-02, Section: B.
- General Note
- Advisor: Wu, Yihong;Guan, Leying.
- Dissertation Note
- Thesis (Ph.D.)--Yale University, 2024.
- Summary, Etc.
- 요약The false discovery rate (FDR) and the false non-discovery rate (FNR), defined as the expected false discovery proportion (FDP) and the false non-discovery proportion (FNP), are the most popular benchmarks for multiple testing. Despite the theoretical and algorithmic advances in recent years, the optimal tradeoff between the FDR and the FNR has been largely unknown except for certain restricted classes of decision rules, e.g., separable rules, or for other performance metrics, e.g., the marginal FDR and the marginal FNR (mFDR and mFNR). In this dissertation, we determine the asymptotically optimal FDR-FNR tradeoff under the two-group random mixture model when the number of hypotheses tends to infinity. Distinct from the optimal mFDR-mFNR tradeoff, which is achieved by separable decision rules, the optimal FDR-FNR tradeoff requires compound rules and randomization even in the large-sample limit. This suboptimality of separable rules holds for other objectives as well, such as maximizing the expected number of true discoveries. To address the limitation of the FDR which only controls the expectations but not the fluctuations of the FDP, we also determine the optimal tradeoff when the FDP is controlled with high probability and show it coincides with that of the mFDR and the mFNR. Extensions to models with a fixed number of non-nulls are also obtained. Finally, a data-driven version of the oracle rule is proposed and applied in an analysis of the multi-omics data for long COVID study that involves large-scale multiple testing.
- Subject Added Entry-Topical Term
- Statistics.
- Index Term-Uncontrolled
- Compound decision rule
- Index Term-Uncontrolled
- False discovery rate
- Index Term-Uncontrolled
- Multiple testing
- Index Term-Uncontrolled
- Long COVID
- Added Entry-Corporate Name
- Yale University Statistics and Data Science
- Host Item Entry
- Dissertations Abstracts International. 86-02B.
- Electronic Location and Access
- 로그인을 한후 보실 수 있는 자료입니다.
- Control Number
- joongbu:657370
MARC
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aNie, Yutong.
■24510▼aFundamental Limits in Large-Scale Multiple Testing and Its Application.
■260 ▼a[S.l.]▼bYale University. ▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a114 p.
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-02, Section: B.
■500 ▼aAdvisor: Wu, Yihong;Guan, Leying.
■5021 ▼aThesis (Ph.D.)--Yale University, 2024.
■520 ▼aThe false discovery rate (FDR) and the false non-discovery rate (FNR), defined as the expected false discovery proportion (FDP) and the false non-discovery proportion (FNP), are the most popular benchmarks for multiple testing. Despite the theoretical and algorithmic advances in recent years, the optimal tradeoff between the FDR and the FNR has been largely unknown except for certain restricted classes of decision rules, e.g., separable rules, or for other performance metrics, e.g., the marginal FDR and the marginal FNR (mFDR and mFNR). In this dissertation, we determine the asymptotically optimal FDR-FNR tradeoff under the two-group random mixture model when the number of hypotheses tends to infinity. Distinct from the optimal mFDR-mFNR tradeoff, which is achieved by separable decision rules, the optimal FDR-FNR tradeoff requires compound rules and randomization even in the large-sample limit. This suboptimality of separable rules holds for other objectives as well, such as maximizing the expected number of true discoveries. To address the limitation of the FDR which only controls the expectations but not the fluctuations of the FDP, we also determine the optimal tradeoff when the FDP is controlled with high probability and show it coincides with that of the mFDR and the mFNR. Extensions to models with a fixed number of non-nulls are also obtained. Finally, a data-driven version of the oracle rule is proposed and applied in an analysis of the multi-omics data for long COVID study that involves large-scale multiple testing.
■590 ▼aSchool code: 0265.
■650 4▼aStatistics.
■653 ▼aCompound decision rule
■653 ▼aFalse discovery rate
■653 ▼aMultiple testing
■653 ▼aLong COVID
■690 ▼a0463
■71020▼aYale University▼bStatistics and Data Science.
■7730 ▼tDissertations Abstracts International▼g86-02B.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160442▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
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