Multiple testing via successive subdivision

TL;DR

This paper generalizes a sequential multiple testing method that identifies significant regions while controlling familywise error, with potential applications in various fields.

Contribution

It formalizes a general version of Heinrich, Bach, and Kornmeier's procedure and proves its familywise error control.

Findings

The generalized procedure controls familywise error rate.

It can be applied to identify regions with significant departures from null hypotheses.

Potential applications include multiple testing scenarios in various domains.

Abstract

A sequential multiple testing procedure recently introduced by Heinrich, Bach and Kornmeier allows to "zoom in" on, and thus identify regions with highly significant departures from null-hypotheses. The purpose of this note is to state a cognate of this procedure in general form and to prove that it controls the familywise error. Two possible applications are briefly indicated.