Hommel's procedure in linear time

Rosa J Meijer; Thijmen J P Krebs; Jelle J Goeman

doi:10.1002/bimj.201700316

Hommel's procedure in linear time

Biom J. 2019 Jan;61(1):73-82. doi: 10.1002/bimj.201700316. Epub 2018 Sep 5.

Authors

Rosa J Meijer¹, Thijmen J P Krebs², Jelle J Goeman³

Affiliations

¹ Statistics Netherlands, Postbus, HA Den Haag, The Netherlands.
² Delft University of Technology, Mekelweg 4, CD Delft, The Netherlands.
³ Biomedical Data Sciences, Leiden University Medical Center, Postbus, RC Leiden, The Netherlands.

PMID: 30187522
DOI: 10.1002/bimj.201700316

Abstract

Hommel's and Hochberg's procedures for familywise error control are both derived as shortcuts in a closed testing procedure with the Simes local test. Hommel's shortcut is exact but takes quadratic time in the number of hypotheses. Hochberg's shortcut takes only linear time after the P-values are sorted, but is conservative. In this paper, we present an exact shortcut in linear time on sorted P-values, combining the strengths of both procedures. The novel shortcut also applies to a robust variant of Hommel's procedure that does not require the assumption of the Simes inequality.

Keywords: Hochberg; close testing; convex hull; simes.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Linear Models
Research Design
Statistics as Topic / methods*