Arithmetics with multiple testing procedures
Year: 2016
Type: preprint
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: monotonic and well-behaved procedures. This article investigates to which extent the classes of (monotonic and 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 and 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 (monotonic and well-behaved) step-up and step-down procedures are closed under taking the union or intersection, but not the complement or difference.
Source: arXiv (Cornell University)
Author: Georg Hahn
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2485002568