Sequentially rejective pairwise testing procedures
type: Item
instance of: scholarly article
title: Sequentially rejective pairwise testing procedures
zbMATH Open document ID: 0654.62069
DOI: 10.1016/0378-3758(87)90112-1
author: Michele Conforti
author: Yosef Hochberg
published in: Journal of Statistical Planning and Inference
publication date: 1987-01-01T00:00:00Z
review text: \textit{S. Holm}'s sequentially rejective procedure [Scand. J. Stat., Theory Appl. 6, 65-70 (1979; Zbl 0402.62058)] was developed for families of hypotheses which allow `free combinations'. Two modifications of Holm's procedure for the family of pairwise hypotheses were discussed by \textit{P. J. Shaffer} [see J. Am. Stat. Assoc. 81, 826-831 (1986; Zbl 0603.62087)]. However, the more powerful modification is only illustrated for the case \(k=4\) means and not discussed further because of the prohibitive computational effort it requires even when k is moderate. We first note that Shaffer's powerful sequentially rejective procedure is equivalent to \textit{E. Peritz}'s [A note on multiple comparisons. Unpublished paper. Hebrew Univ. (1970)] closed testing scheme when a natural relation holds between the corresponding critical values. This raises the question of whether conditions exist under which a computationally efficient algorithm can be derived for implementing that procedure. We identified conditions under which a very efficient algorithm is given. The given conditions are quite restrictive but extremely simple to test in each particular case. In developing the algorithm we use a graph theory approach and provide some new results which are potentially of independent theoretical interest.
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62F99
Mathematics Subject Classification ID: 62F25
zbMATH DE Number: 4068110
zbMATH Keywords: sequentially rejective procedure
zbMATH Keywords: pairwise hypotheses
zbMATH Keywords: computationally efficient algorithm
zbMATH Keywords: graph theory approach
MaRDI profile type: Publication
full work available at URL: 0378-3758(87)90112-1
OpenAlex ID: W2055850492
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description: scientific article; zbMATH DE number 4068110