"&agr;"-investing: a procedure for sequential control of expected false discoveries

Dean P. Foster and Robert A. Stine

Journal Of The Royal Statistical Society Series B, 2008, vol. 70, issue 2, pages 429-444

Abstract: "&agr;"-investing is an adaptive sequential methodology that encompasses a large family of procedures for testing multiple hypotheses. All control mFDR, which is the ratio of the expected number of false rejections to the expected number of rejections. mFDR is a weaker criterion than the false discovery rate, which is the expected value of the ratio. We compensate for this weakness by showing that "&agr;"-investing controls mFDR at every rejected hypothesis. "&agr;"-investing resembles "&agr;"-spending that is used in sequential trials, but it has a key difference. When a test rejects a null hypothesis, "&agr;"-investing earns additional probability towards subsequent tests. "&agr;"-investing hence allows us to incorporate domain knowledge into the testing procedure and to improve the power of the tests. In this way, "&agr;"-investing enables the statistician to design a testing procedure for a specific problem while guaranteeing control of mFDR. Copyright (c) 2008 The Authors.

Date: 2008

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