Divergence-based estimation and testing with misclassified data
dc.contributor.author | Landaburu Jiménez, María Elena | |
dc.contributor.author | Morales González, Domingo | |
dc.contributor.author | Pardo Llorente, Leandro | |
dc.date.accessioned | 2023-06-20T09:38:57Z | |
dc.date.available | 2023-06-20T09:38:57Z | |
dc.date.issued | 2005-07 | |
dc.description.abstract | The well-known chi-squared goodness-of-fit test for a multinomial distribution is generally biased when the observations are subject to misclassification. In Pardo and Zografos (2000) the problem was considered using a double sampling scheme and phi-divergence test statistics. A new problem appears if the null hypothesis is not simple because it is necessary to give estimators for the unknown parameters. In this paper the minimum phi-divergence estimators are considered and some of their properties are established. The proposed phi-divergence test statistics are obtained by calculating phi-divergences between probability density functions and by replacing parameters by their minimum phi-divergence estimators in the derived expressions. Asymptotic distributions of the new test statistics are also obtained. The testing procedure is illustrated with an example | |
dc.description.department | Depto. de Estadística e Investigación Operativa | |
dc.description.faculty | Fac. de Ciencias Matemáticas | |
dc.description.refereed | TRUE | |
dc.description.status | pub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/16459 | |
dc.identifier.citation | Ali, S.M. and Silvey, S.D. (1966). A general class of coefficient of divergence of one distribution from another.J. of Royal Statistical Society, Series B 286, 131–142. Birch, M. H. (1964). A new proof of the Pearson-Fisher theorem.Annals of Mathematical Statistics,35, 817–824. Cheng, K. F., Hsueh, H. M. and Chien, T.H. (1998). Goodness of fit tests with misclassified data.Communications in Statistics—Theory and Methods,27, 1379–1393. Csiszár, I. (1963). Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten.Publications of the Mathematical Institute of Hungarian Academy of Sciences,8,Ser. A, 85–108. Cressie, N. and Read, T.R.C. (1984). Multinomial Goodness-of-fit Tests.J. of the Royal Statistical Society, Series B,46, 440–464. Dik, J. J. and Gunst, M. C. M. (1985): The distribution of general quadratic forms in normal variables.Statistica Neerlandica,39, 14–26. Eckler, A. R. (1969): A survey of coverage problems associated with point and area targets.Tecnometrics 11, 561–589. Gupta, S. S. (1963): Bibliography on the multivariate normal integrals and related topics.Annals of Mathematical Statistics 34, 829–838. Imhof, J. P. (1961): Computing the distribution of quadratic forms in normal variables.Biometrika,48, 419–426. Jensen, D. R. and Solomon, H. (1972): A Gaussian approximation to the distribution of a definite quadratic form.J. of the American Statistical Association,67, 898–902. Johnson, N. L. and Kotz, S. (1968): Tables of distributions of positive definite quadratic forms in central normal variables.Sankhya,30, 303–314. Morales, D., Pardo, L. and Vajda, I. (1995): Asymptotic divergence of estimates of discrete distributions.J. of Statistical Planning and Inference,48, 347–369. Pardo, L. and Zografos K. (2000): Goodness of fit tests with misclassified data based on ø-divergences.Biometrical Journal,42, 223–237. Rao, J. N. K. and Scott, A. J. (1981): The Analysis of categorical data from complex sample surveys: Chi-squared tests for goodness-of-fit and independence in two-way tables.J. of the American Statistical Association,76, 221–230. Read, R. C. and Cressie, N. A. C. (1988).Goodness-of-fit Statistics for Discrete Multivariate Data, Springer Verlag, New York. Satterhwaite, F. E. (1946): An approximation distribution of estimates of variance components.Biometrics,2, 110–114. Solomon, H. (1960): Distribution of quadratic forms-tables and applications, Technical Report 45, Applied Mathematics and statistics laboratories, Stanford University, Stanford, CA. Tenenbein, A. (1970): A double sampling scheme for estimating from binomial data with misclassification.J. of the American Statistical Association,65, 1350–1361. Tenenbein, A. (1971). A double sampling scheme for estimating from binomial data with misclassification: Sample size and determination.Biometrics,27, 935–944. Tenenbein, A. (1972). A double sampling scheme for estimating from misclassified multinomial data with applications to sampling inspection.Technometrics,14, 187–202. | |
dc.identifier.doi | 10.1007/BF02762841 | |
dc.identifier.issn | 0932-5026 | |
dc.identifier.officialurl | http://www.springerlink.com/content/j151063g0r87lg10/fulltext.pdf | |
dc.identifier.relatedurl | http://www.springerlink.com/ | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/50109 | |
dc.issue.number | 3 | |
dc.journal.title | Statistical Papers | |
dc.language.iso | eng | |
dc.page.final | 409 | |
dc.page.initial | 397 | |
dc.publisher | Springer Verlag | |
dc.relation.projectID | BMF2000-0800 | |
dc.rights.accessRights | restricted access | |
dc.subject.cdu | 519.24 | |
dc.subject.keyword | Misclassification | |
dc.subject.keyword | Double sampling | |
dc.subject.keyword | Divergence estimators | |
dc.subject.keyword | Goodness-of-fit tests | |
dc.subject.keyword | Divergence statistics | |
dc.subject.ucm | Muestreo (Estadística) | |
dc.subject.unesco | 1209.10 Teoría y Técnicas de Muestreo | |
dc.title | Divergence-based estimation and testing with misclassified data | |
dc.type | journal article | |
dc.volume.number | 46 | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 0cf1bfef-b105-422e-9f20-80ca13261ed7 | |
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relation.isAuthorOfPublication | a6409cba-03ce-4c3b-af08-e673b7b2bf58 | |
relation.isAuthorOfPublication.latestForDiscovery | 0cf1bfef-b105-422e-9f20-80ca13261ed7 |
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