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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 서양
- 최종처리일시
- 20250211151020
- ISBN
- 9798383565728
- DDC
- 310
- 저자명
- Nie, Yutong.
- 서명/저자
- Fundamental Limits in Large-Scale Multiple Testing and Its Application
- 발행사항
- [Sl] : Yale University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 114 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-02, Section: B.
- 주기사항
- Advisor: Wu, Yihong;Guan, Leying.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2024.
- 초록/해제
- 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.
- 일반주제명
- Statistics
- 키워드
- Multiple testing
- 키워드
- Long COVID
- 기타저자
- Yale University Statistics and Data Science
- 기본자료저록
- Dissertations Abstracts International. 86-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
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[Sl]▼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.
