Minimum divergence estimators based on grouped data

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dc.contributor.authorMenéndez Calleja, María Luisa
dc.contributor.authorMorales González, Domingo
dc.contributor.authorPardo Llorente, Leandro
dc.contributor.authorVadja, Igor
dc.date.accessioned2023-06-20T17:09:34Z
dc.date.available2023-06-20T17:09:34Z
dc.date.issued2001-06
dc.description.abstractThe paper considers statistical models with real-valued observations i.i.d. by F(x, theta (0)) from a family of distribution functions (F(x, theta); theta is an element of Theta), Theta subset of R-s, s greater than or equal to 1. For random quantizations defined by sample quantiles (F-n(-1)(lambda (1)),..., F-n(-1)(lambda (m-1))) of arbitrary fixed orders 0 < <lambda>(1) < ... < lambda (m-1) < 1, there are studied estimators <theta>(phi ,n) of theta (0) which minimize phi -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F-1(lambda (1), theta (0)),..., F-1(lambda (m-1), theta (0))). Moreover, the Fisher information matrix I-m(theta (0), lambda) of the latter model with the equidistant orders lambda = (lambda (j) = j/m : 1 less than or equal to j less than or equal to m-1) arbitrarily closely approximates the Fisher information F(theta (0)) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipSabbatical Program of Complutense University of Madrid
dc.description.sponsorshipCACR
dc.description.sponsorshipDGI
dc.description.sponsorshipCV
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/18053
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dc.identifier.doi10.1023/A:1012466605316
dc.identifier.issn0020-3157
dc.identifier.officialurlhttp://www.springerlink.com/content/v23715631067773m/fulltext.pdf
dc.identifier.relatedurlhttp://www.springerlink.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57864
dc.issue.number2
dc.journal.titleAnnals of the Institute of Statistical Mathematics
dc.language.isoeng
dc.page.final288
dc.page.initial277
dc.publisherSpringer
dc.relation.projectID102/99/1137
dc.relation.projectIDBFM 2000-0800
dc.relation.projectID99-159-1-01. 277
dc.rights.accessRightsrestricted access
dc.subject.cdu519.2
dc.subject.keywordminimum divergence estimators
dc.subject.keywordrandom quantization
dc.subject.keywordasymptotic normality
dc.subject.keywordefficiency
dc.subject.keywordFisher information
dc.subject.keywordoptimization
dc.subject.ucmEstadística aplicada
dc.titleMinimum divergence estimators based on grouped data
dc.typejournal article
dc.volume.number53
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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