Elementary proofs of several results on false discovery rate

TL;DR

This paper provides simple, self-contained proofs for key results related to false discovery rate control methods like BH, BY, and e-BH procedures, including their dependencies and inequalities.

Contribution

It offers elementary, accessible proofs for complex FDR results, enhancing understanding and teaching of these statistical procedures.

Findings

Elementary proofs for FDR control results

Extensions to dependent p-values and e-values

Derivation of inequalities for Simes and Hommel

Abstract

We collect self-contained elementary proofs of four 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 correction 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.