A structure theorem on bivariate positive quadrant dependent distributions and tests for independence in two-way contingency tables
type: Item
instance of: scholarly article
title: A structure theorem on bivariate positive quadrant dependent distributions and tests for independence in two-way contingency tables
zbMATH Open document ID: 0627.62056
DOI: 10.1016/0047-259X(87)90180-1
author: M. Bhaskara Rao
author: P. R. Krishnaiah
author: K. Subramanyam
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: In this paper, the set of all bivariate positive quadrant dependent distributions with fixed marginals is shown to be compact and convex. Extreme points of this convex set are enumerated in some specific examples. Applications are given in testing the hypothesis of independence against strict positive quadrant dependence in the context of ordinal contingency tables. The performance of two tests, one of which is based on eigenvalues of a random matrix, is compared. Various procedures based upon certain functions of the eigenvalues of a random matrix are also proposed for testing for independence in a two-way contingency table when the marginals are random.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62H17
zbMATH DE Number: 4020234
zbMATH Keywords: asymptotic distributions
zbMATH Keywords: compact set
zbMATH Keywords: gamma ratio
zbMATH Keywords: power function
zbMATH Keywords: bivariate positive quadrant dependent distributions
zbMATH Keywords: fixed marginals
zbMATH Keywords: Extreme points
zbMATH Keywords: convex set
zbMATH Keywords: hypothesis of independence
zbMATH Keywords: strict positive quadrant dependence
zbMATH Keywords: ordinal contingency tables
zbMATH Keywords: eigenvalues of a random matrix
zbMATH Keywords: two-way contingency table
MaRDI profile type: Publication
cites work: Q3792078
cites work: Q5560061
cites work: A review of selected topics in multivariate probability inequalities
cites work: Asymptotic expansions for the distributions of some functions of the latent roots of matrices in three situations
cites work: The analysis of cross-classified data having ordered and/or unordered categories: Association models, correlation models, and asymmetry models for contingency tables with or without missing entries
cites work: Measures of association for cross classifications
cites work: Q4110164
cites work: Duality theorems for marginal problems
cites work: A note on the joint distribution of correlated quadratic forms
cites work: Q3906265
cites work: Q3911889
cites work: The Structure of Bivariate Distributions
cites work: Q5588236
cites work: TESTS OF SIGNIFICANCE FOR THE LATENT ROOTS OF COVARIANCE AND CORRELATION MATRICES
cites work: Some Concepts of Dependence
cites work: Partitioning of interaction in analysis of variance
cites work: Q3793548
cites work: ASYMPTOTIC DISTRIBUTIONS OF THE CANONICAL CORRELATIONS FROM CONTINGENCY TABLES
cites work: Q4197903
cites work: A Note on the Canonical Correlations From Contingency Tables
cites work: Q5508589
cites work: THE INTERPRETATION OF INTERACTIONS IN FACTORIAL EXPERIMENTS
cites work: Q3940666
cites work: Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations
cites work: On the asymptotic joint distributions of certain functions of the eigenvalues of four random matrices
full work available at URL: 0047-259x(87)90180-1
OpenAlex ID: W2046403689
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description: scientific article; zbMATH DE number 4020234