Components of Pearson's statistic for at least partially ordered m-way contingency tables
type: Item
instance of: scholarly article
title: Components of Pearson's statistic for at least partially ordered m-way contingency tables
zbMATH Open document ID: 1175.62043
DOI: 10.1155/2009/980706
author: John C. W. Rayner
author: Eric J. Beh
published in: Journal of Applied Mathematics and Decision Sciences
publication date: 2009-11-23T00:00:00Z
full work available at URL: https://eudml.org/doc/225141
review text: Summary: For at least partially ordered three-way tables, it is well known how to arithmetically decompose Pearson's \(X_{P}^{2}\) statistic into informative components that enable a close scrutiny of the data. Similarly, well-known are smooth models for two-way tables from which score tests for homogeneity and independence can be derived. From these models, both the components of Pearson's \(X_{P}^{2}\) and information about their distributions can be derived. Two advantages of specifying models are first that the score tests have weak optimality properties and second that identifying the appropriate model from within a class of possible models gives insights about the data. Here, smooth models for higher-order tables are given explicitly, as are the partitions of Pearson's \(X_{P}^{2}\) into components. The asymptotic distributions of statistics related to the components are also addressed.
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62H17
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 5637306
Wikidata QID: Q58646868
MaRDI profile type: Publication
OpenAlex ID: W2099286865
cites work: Partitioning Pearson's Chi-Squared Statistic for a Completely Ordered Three-Way Contingency Table
cites work: Partitioning Pearson's chi-squared statistic for a partially ordered three-way contingency table
cites work: Q5588236
cites work: Locally asymptotically most stringent tests and Lagrangian multiplier tests of linear hypotheses
description: scientific article; zbMATH DE number 5637306