Tests based on divergences for and against ordered alternatives in cubic contingency tables

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dc.contributor.authorMenéndez Calleja, María Luisa
dc.contributor.authorMorales González, Domingo
dc.contributor.authorPardo Llorente, Leandro
dc.date.accessioned2023-06-20T09:45:38Z
dc.date.available2023-06-20T09:45:38Z
dc.date.issued2003-01-25
dc.description.abstractCubic contingency tables arise frequently in medical sciences when individuals are measured before, during and after the application of some treatment for a given illness, and data are recorded on an ordered categorical scale. By assigning increasing values to the levels of the illness, the efficiency of the medical treatment can be checked by testing for a given ordering of the cell probabilities p(ijk)'s. One possibility is to consider the hypothesis H-1 that p(ijk) less than or equal to p(i'j'f') if and only if (i', j', k') can be obtained from (i, j, k) through successive pairwise interchanges of adjacent components resulting each time in a decreasing order of the two interchanged components. In this paper we introduce two families of divergence statistics to test for and against H-1, and their asymptotic distributions are obtained. It is also shown that likelihood-ratio test statistics of Barmi and Zimmermann [Statist. Prob. Lett. 45 (1999) 1] are included in these families.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/17834
dc.identifier.citationI. Csiszár, Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizit€at von Markoffschen Ketter, Math. Inst. Hung. Acad. Sci., Series A, 8 (1963) 84– 108. S.M. Ali, S.D. Silvey, A general class of coefficients of divergence of one distribution from another, J. Roy. Statist. Soc. B 28 (1966) 131–142. H.E. Barmi, S.C. Kochar, Likelihood ratio tests for symmetry against ordered alternatives in a square contingency table, Statist. Probab. Lett. 2 (1995) 167–173. H.E. Barmi, D. Zimmermann, Likelihood ratio tests for and against decreasing in transposition in K x K x K contingency tables, Statist. Probab. Lett. 45 (1999) 1–10. F. Liese, I. Vajda, Convex Statistical Distances, Teubner, Leipzig, 1987. M.L. Menéndez, J.A. Pardo, L. Pardo, Tests based on phi-divergences for bivariate symmetry, Metrika 53 (2001) 15–29. T. Robertson, F.T. Wright, R.L. Dykstra, Order Restricted Statistical Inference, Wiley, New York, 1988. I. Vajda, Theory of Statistical Inference and Information, Kluwer Academic Publishers, Boston, MA, 1989
dc.identifier.doi10.1016/S0096-3003(01)00214-4
dc.identifier.issn0096-3003
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0096300301002144
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50315
dc.issue.number2-3
dc.journal.titleApplied Mathematics and Computation
dc.language.isoeng
dc.page.final213
dc.page.initial207
dc.publisherElsevier
dc.rights.accessRightsrestricted access
dc.subject.cdu519.2
dc.subject.keywordcontingency table
dc.subject.keywordphi-divergence measure
dc.subject.keywordchi-bar square
dc.subject.keywordordered cell probabilities.
dc.subject.ucmEstadística aplicada
dc.titleTests based on divergences for and against ordered alternatives in cubic contingency tables
dc.typejournal article
dc.volume.number134
dspace.entity.typePublication
relation.isAuthorOfPublication4d5cedd9-975b-43fb-bc2e-f55dec36a2bf
relation.isAuthorOfPublicationa6409cba-03ce-4c3b-af08-e673b7b2bf58
relation.isAuthorOfPublication.latestForDiscovery4d5cedd9-975b-43fb-bc2e-f55dec36a2bf
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