Large sample results for tests of association ii. multinomial and stratified sampling

Kulinskaya, Elena (1995) Large sample results for tests of association ii. multinomial and stratified sampling. Communications in Statistics: Theory and Methods, 24 (5). pp. 1121-1150. ISSN 0361-0926

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Abstract

This paper deals with the asymptotics of a class of tests for association in 2-way contingency tables based on square forms in cell frequencies, given the total number of observations (multinomial sampling) or one set of marginal totals (stratified sampling). The case when both row and column marginal totals are fixed (hypergeometric sampling) was studied in Kulinskaya (1994), The class of tests under consideration includes a number of classical measures for association, Its two subclasses are the tests based on statistics using centralized cell frequencies (asymptotically distributed as weighted sums of central chi-squares) and those using the non-centralized cell frequencies (asymptotically normal). The parameters of asymptotic distributions depend on the sampling model and on true marginal probabilities. Maximum efficiency for asymptotically normal statistics is achieved under hypergeometric sampling, If the cell frequencies or the statistic as a whole are centralized using marginal proportions as estimates for marginal probabilities, the asymptotic distribution does not differ much between models and it is equivalent to that under hypergeometric sampling. These findings give an extra justification for the use of permutation tests for association (which are based on hypergeometric sampling). As an application, several well known measures of association are analysed.

Item Type:	Article
Uncontrolled Keywords:	association,contingency table,partition,multinomial sampling,stratified sampling,asymptotics of tests
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Norwich Epidemiology Centre Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre Faculty of Science > Research Groups > Data Science and Statistics Faculty of Medicine and Health Sciences > Research Centres > Business and Local Government Data Research Centre (former - to 2023)
Depositing User:	Pure Connector
Date Deposited:	04 Jul 2014 12:51
Last Modified:	01 May 2024 10:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/48969
DOI:	10.1080/03610929508831544

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