Date of Award
Spring 2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Statistics and Data Science
First Advisor
Wu, Yihong
Abstract
The 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.
Recommended Citation
Nie, Yutong, "Fundamental Limits in Large-Scale Multiple Testing and Its Application" (2024). Yale Graduate School of Arts and Sciences Dissertations. 1332.
https://elischolar.library.yale.edu/gsas_dissertations/1332
