On the Simes inequality and its generalization

TL;DR

This paper revisits and strengthens the Simes inequality and its generalization, providing clearer understanding and a simpler proof relevant to multiple hypothesis testing procedures.

Contribution

It clarifies and strengthens the classic Simes inequality and offers an alternative, simpler proof for its recent generalization.

Findings

Revised and strengthened the Simes inequality.

Provided a simpler proof for the generalized inequality.

Enhanced understanding of multiple hypothesis testing methods.

Abstract

The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and strengthen it and a recently proposed generalization of it to offer an alternative simpler proof.