Elementary proofs of four standard results on false discovery rate

01/23/2022

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by   Ruodu Wang, et al.

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We collect self-contained elementary proofs of four standard results in the literature on the false discovery rate of the Benjamini-Hochberg (BH) procedure for independent or positive-regression dependent p-values, the Benjamini-Yekutieli procedure for arbitrarily dependent p-values, and the e-BH procedure for arbitrarily dependent e-values. As a corollary, the above proofs also lead to some inequalities of Simes and Hommel.