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Abstract:
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We propose alpha investing, an adaptive, sequential methodology for testing multiple hypotheses. Alpha investing encompasses a large family of rules for testing multiple hypotheses, all having the Property that the mFDR is controlled. mFDR, which is the ratio of the expected number of false rejections to the expected number of rejections, is a weaker criterion than the FDR, which is the expected value of the ratio. We partially compensate for this weakness by showing that alpha-investing rules have a stronger martingale property that offers control of the procedure beyond mFDR. Alpha-investing rules mimic alpha-spending rules used in sequential trials, but possess a key difference. When a test rejects a null hypothesis, alpha-investing rules earn additional probability toward subsequent tests.
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