On rank statistics: An approach via metrics on the permutation group
type: Item
instance of: scholarly article
title: On rank statistics: An approach via metrics on the permutation group
zbMATH Open document ID: 0770.62036
DOI: 10.1016/0378-3758(92)90015-K
author: D. E. Critchlow
published in: Journal of Statistical Planning and Inference
publication date: 1993-01-16T00:00:00Z
review text: This paper gives a general method to generate rank test statistics for two-sample or multisample problems using different metrics on the permutation group w.r.t. which rank tests are invariant. Some well-known tests such as Kendall's tau, Spearman's rho and Spearman's footrule are already well-known but use of the Hamming distance and the Ulam distance is a novel one. This method is applied systematically to: (i) the location problem --- one-sample, two-sample and multisample situation, (ii) the two-sample dispersion problem with equal medians, (iii) the two-way layout problem and (iv) the problem of testing for trend. The paper also derives some combinatorial and group theoretic properties of the above metrics that play a key role in the computation of the corresponding test statistics.
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 95636
zbMATH Keywords: metrics on permutations
zbMATH Keywords: induced rank test statistic
zbMATH Keywords: invariance
zbMATH Keywords: subgroups of permutations
zbMATH Keywords: quotient space
zbMATH Keywords: multisample problems
zbMATH Keywords: Kendall's tau
zbMATH Keywords: Spearman's rho
zbMATH Keywords: Spearman's footrule
zbMATH Keywords: Hamming distance
zbMATH Keywords: Ulam distance
zbMATH Keywords: location problem
zbMATH Keywords: two-sample dispersion problem with equal medians
zbMATH Keywords: two-way layout problem
zbMATH Keywords: testing for trend
reviewed by: B. K. Kale
MaRDI profile type: Publication
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full work available at URL: 0378-3758(92)90015-k
OpenAlex ID: W2047229167
description: scientific article; zbMATH DE number 95636