Analysis of odds ratios in \(2\times n\) ordinal contingency tables
type: Item
instance of: scholarly article
title: Analysis of odds ratios in \(2\times n\) ordinal contingency tables
zbMATH Open document ID: 0659.62065
DOI: 10.1016/0047-259X(88)90143-1
author: K. Subramanyam
author: M. Bhaskara Rao
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: The set of all bivariate probability distributions with support contained in \(\{(i,j); i=1,2 \text{ and } j=1,2,\dots,n\}\) which are totally positive of order two is shown to be a convex set under some conditions on one of the marginal distributions. The extreme points of this compact convex set are explicitly enumerated. Using the structure of this convex set, we show that the power function of any test for testing the hypothesis of independence against the hypothesis of strict total positivity of order two in \(2\times n\) ordinal contingency tables has a simple form in terms of the extreme points. A numerical illustration is provided.
Mathematics Subject Classification ID: 62H17
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 4078536
zbMATH Keywords: Goodman-Kruskal's gamma ratio
zbMATH Keywords: identifiability of mixtures
zbMATH Keywords: odds ratio
zbMATH Keywords: positive likelihood ratio dependence
zbMATH Keywords: marginal distributions
zbMATH Keywords: extreme points
zbMATH Keywords: compact convex set
zbMATH Keywords: power function
zbMATH Keywords: hypothesis of independence
zbMATH Keywords: hypothesis of strict total positivity of order two
zbMATH Keywords: ordinal contingency tables
MaRDI profile type: Publication
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full work available at URL: 0047-259x(88)90143-1
OpenAlex ID: W2091737710
description: scientific article; zbMATH DE number 4078536