Stepwise Multiple Testing as Formalized Data Snooping
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. In addition, we advocate the use of studentization when it is feasible. 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. We present our methodology in the context of comparing several strategies to a common benchmark and deciding which strategies actually beat the benchmark. However, our ideas can easily be extended and/or modified to other contexts, such as making inference for the individual regression coefficients in a multiple regression framework. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.
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