Closure properties of classes of multiple testing procedures

Hahn, Georg (2018) Closure properties of classes of multiple testing procedures. AStA Advances in Statistical Analysis, 102 (2). pp. 167-178. ISSN 1863-8171

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Abstract

Statistical discoveries are often obtained through multiple hypothesis testing. A variety of procedures exists to evaluate multiple hypotheses, for instance the ones of Benjamini-Hochberg, Bonferroni, Holm or Sidak. We are particularly interested in multiple testing procedures with two desired properties: (solely) monotonic and well-behaved procedures. This article investigates to which extent the classes of (monotonic or well-behaved) multiple testing procedures, in particular the subclasses of so-called step-up and step-down procedures, are closed under basic set operations, specifically the union, intersection, difference and the complement of sets of rejected or non-rejected hypotheses. The present article proves two main results: First, taking the union or intersection of arbitrary (monotonic or well-behaved) multiple testing procedures results in new procedures which are monotonic but not well-behaved, whereas the complement or difference generally preserves neither property. Second, the two classes of (solely monotonic or well-behaved) step-up and step-down procedures are closed under taking the union or intersection, but not the complement or difference.

Item Type:
Journal Article
Journal or Publication Title:
AStA Advances in Statistical Analysis
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
89692
Deposited By:
Deposited On:
15 Jan 2018 10:14
Refereed?:
Yes
Published?:
Published
Last Modified:
09 Sep 2020 04:36