The Optimal Discovery Procedure: A New Approach to Simultaneous Significance Testing
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最优发现程序：同时显著性检验的新方法
- 研究问题
- 多重显著性检验能否借用各检验之间的信息，在固定预期假阳性数量时最大化预期真阳性数量，而非分别评估各项检验？
- 方法与思路
- 作者提出最优发现程序，研究其与错误发现率最优性的联系，并以多个正态均值的同时检验展示跨检验信息借用。
- 材料陈述的贡献
- 摘要称该程序在固定预期假阳性数下最大化预期真阳性数，并展示正态均值例子中优于逐项最优检验的同时程序。
- 阅读关注点
- 全文需核对最优性要求的分布信息、跨检验关系及可实现方式，并区分预期假阳性数约束与错误发现率控制的具体联系。
- 阅读边界
- 仅据 Crossref 摘要；未给出完整最优性条件或实际估计步骤，预期假阳性数约束不能直接当作任意依赖下的错误发现率保证。
原文摘要
Summary The Neyman–Pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known. This result has played a major role in the development of significance testing strategies that are used in practice. Most of the work extending single-testing strategies to multiple tests has focused on formulating and estimating new types of significance measures, such as the false discovery rate. These methods tend to be based on p-values that are calculated from each test individually, ignoring information from the other tests. I show here that one can improve the overall performance of multiple significance tests by borrowing information across all the tests when assessing the relative significance of each one, rather than calculating p-values for each test individually. The ‘optimal discovery procedure’ is introduced, which shows how to maximize the number of expected true positive results for each fixed number of expected false positive results. The optimality that is achieved by this procedure is shown to be closely related to optimality in terms of the false discovery rate. The optimal discovery procedure motivates a new approach to testing multiple hypotheses, especially when the tests are related. As a simple example, a new simultaneous procedure for testing several normal means is defined; this is surprisingly demonstrated to outperform the optimal single-test procedure, showing that a method which is optimal for single tests may no longer be optimal for multiple tests. Connections to other concepts in statistics are discussed, including Stein's paradox, shrinkage estimation and the Bayesian approach to hypothesis testing.