Stepwise Multiple Testing as Formalized Data Snooping
提出一种逐步多重检验方法，能渐近控制族系错误率，比单步法更有效拒绝错误假设，并通过学生化处理捕捉统计量的联合依赖结构，适用于比较多个策略是否优于共同基准等场景。
It is common in econometric applications that several hypothesis tests are\ncarried out at the same time. The problem then becomes how to decide which\nhypotheses to reject, accounting for the multitude of tests. In this paper,\nwe suggest a stepwise multiple testing procedure which asymptotically\ncontrols the familywise error rate at a desired level. Compared to related\nsingle-step methods, our procedure is more powerful in the sense that it\noften will reject more false hypotheses. In addition, we advocate the use\nof studentization when it is feasible. Unlike some stepwise methods, our\nmethod implicitly captures the joint dependence structure of the test\nstatistics, which results in increased ability to detect alternative\nhypotheses. We prove our method asymptotically controls the familywise error\nrate under minimal assumptions. We present our methodology in the context of\ncomparing several strategies to a common benchmark and deciding which\nstrategies actually beat the benchmark. However, our ideas can easily be\nextended and/or modied to other contexts, such as making inference for the\nindividual regression coecients in a multiple regression framework. Some\nsimulation studies show the improvements of our methods over previous \nproposals. We also provide an application to a set of real data.