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Closure properties of classes of multiple testing procedures

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Closure properties of classes of multiple testing procedures. / Hahn, Georg.
In: AStA Advances in Statistical Analysis, Vol. 102, No. 2, 04.2018, p. 167-178.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Hahn, G 2018, 'Closure properties of classes of multiple testing procedures', AStA Advances in Statistical Analysis, vol. 102, no. 2, pp. 167-178. https://doi.org/10.1007/s10182-017-0297-0

APA

Hahn, G. (2018). Closure properties of classes of multiple testing procedures. AStA Advances in Statistical Analysis, 102(2), 167-178. https://doi.org/10.1007/s10182-017-0297-0

Vancouver

Hahn G. Closure properties of classes of multiple testing procedures. AStA Advances in Statistical Analysis. 2018 Apr;102(2):167-178. Epub 2017 May 5. doi: 10.1007/s10182-017-0297-0

Author

Hahn, Georg. / Closure properties of classes of multiple testing procedures. In: AStA Advances in Statistical Analysis. 2018 ; Vol. 102, No. 2. pp. 167-178.

Bibtex

@article{ffe681442cfc467fb4dd50042d230877,
title = "Closure properties of classes of multiple testing procedures",
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.",
keywords = "math.ST, stat.TH, Multiple hypothesis testing, Statistical significance , Step-up procedure, Set operations, Monotonicity",
author = "Georg Hahn",
year = "2018",
month = apr,
doi = "10.1007/s10182-017-0297-0",
language = "English",
volume = "102",
pages = "167--178",
journal = "AStA Advances in Statistical Analysis",
issn = "1863-8171",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Closure properties of classes of multiple testing procedures

AU - Hahn, Georg

PY - 2018/4

Y1 - 2018/4

N2 - 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.

AB - 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.

KW - math.ST

KW - stat.TH

KW - Multiple hypothesis testing

KW - Statistical significance

KW - Step-up procedure

KW - Set operations

KW - Monotonicity

U2 - 10.1007/s10182-017-0297-0

DO - 10.1007/s10182-017-0297-0

M3 - Journal article

VL - 102

SP - 167

EP - 178

JO - AStA Advances in Statistical Analysis

JF - AStA Advances in Statistical Analysis

SN - 1863-8171

IS - 2

ER -