Stepwise Multiple Testing as Formalized Data Snooping

TLDR: In this paper, a stepwise multiple testing procedure is proposed to asymptotically control the familywise error rate at a desired level, which implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect alternative hypotheses.

Abstract: It is common in econometric applications that several hypothesis tests are carried out at the same time. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. In this paper, we suggest a stepwise multiple testing procedure which asymptotically controls the familywise error rate at a desired level. Compared to related single-step methods, our procedure is more powerful in the sense that it often will reject more false hypotheses. Unlike some stepwise methods, our method implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect alternative hypotheses. We prove our method asymptotically controls the familywise error rate under minimal assumptions. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.