Minimum phi-divergence estimator and hierarchical testing in loglinear models

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dc.contributor.authorCressie, Noel A.
dc.contributor.authorPardo Llorente, Leandro
dc.date.accessioned2023-06-20T17:09:42Z
dc.date.available2023-06-20T17:09:42Z
dc.date.issued2000-07
dc.description.abstractIn this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum phi-divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a phi-divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the problem of testing a nested sequence of loglinear models.
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/18082
dc.identifier.citationAgresti, A. (1996). An Introduction to Categorical Data Analysis. John Wiley, New York. Christensen, R. (1997). Log-Linear Model and Logistic Regression. Springer-Verlag, New York. Collett, D. (1994). Modelling Survival Data in Medical Research. Chapman and Hall, London. Cornfield, J. (1962). Joint dependence of risk of coronary heart disease on serum cholesterol and systolic blood pressure: a discriminant function analysis. Federation Proceedings 21, 58–61. Cressie, N. and Read, T. R. C. (1984). Multinomial goodness-of-fit tests. J. Roy. Statist. Soc. Ser. B 46, 440–464. Csiszar, I. (1967). Information type measures of difference of probability distributions and indirect observations. Studia Scientiarum Mathematicarum Hungarica 2, 105–113. Medak, F. M. and Cressie, N. (1991). Hierarchical testing of parametric models using the power-divergence family of test statistics. Statistical Laboratory Preprint, No. 91-14, Iowa State University, Ames, IA. Menéndez, M. L., Morales, D. and Pardo, L. (1997). φ -divergences and nested models. Appl. Math. Lett. 10, 129–132. Morales, D., Pardo, L. and Vajda, I. (1995). Asymptotic divergences of estimates of discrete distributions. J. Statist. Plann. Inference 48, 347–369. Morales, D., Pardo, L. and Vajda, I. (1997). Some new statistics for testing hypotheses in parametric models. J. Multivariate Anal. 62, 137–168. Pardo, M. C. (1999). Estimation of parameters for a mixture of normal distributions on the basis of the Cressie and Read divergence. Comm. Statist. Simulation Comput. 28, 115–130. Read, T. R. C. and Cressie, N. A. C. (1988). Goodness-of-fit Statistics for Discrete Multivariate Data. Springer-Verlag, New York. Statgraphics Plus (1993). Statistical Graphics System by Statistical Graphics Corporation: Reference Manual, Version 7 for DOS. Manugistics Inc. Rockville, MD.
dc.identifier.issn1017-0405
dc.identifier.officialurlhttp://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n310.pdf
dc.identifier.relatedurlhttp://www3.stat.sinica.edu.tw/statistica/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57868
dc.issue.number3
dc.journal.titleStatistica Sinica
dc.language.isoeng
dc.page.final884
dc.page.initial867
dc.publisherStatistica sinica
dc.rights.accessRightsopen access
dc.subject.cdu519.21
dc.subject.keywordasymptotic distributions
dc.subject.keywordFraminghan heart study
dc.subject.keywordmultinomial distribution
dc.subject.keywordnested hypotheses
dc.subject.keywordpower divergence
dc.subject.keywordRenyi divergence
dc.subject.keyworddistributions
dc.subject.ucmProbabilidades (Matemáticas)
dc.titleMinimum phi-divergence estimator and hierarchical testing in loglinear models
dc.typejournal article
dc.volume.number10
dspace.entity.typePublication
relation.isAuthorOfPublicationa6409cba-03ce-4c3b-af08-e673b7b2bf58
relation.isAuthorOfPublication.latestForDiscoverya6409cba-03ce-4c3b-af08-e673b7b2bf58
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