Stepwise Multiple Testing as Formalized Data Snooping

Abstract

In econometric applications, often several hypothesis tests are carried out at once. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. This paper suggests a stepwise multiple testing procedure that asymptotically controls the familywise error rate. Compared to related single-step methods, the procedure is more powerful and often will reject more false hypotheses. In addition, we advocate the use of studentization when feasible. Unlike some stepwise methods, the method implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect false hypotheses. The methodology is presented in the context of comparing several strategies to a common benchmark. However, our ideas can easily be extended to other contexts where multiple tests occur. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.