Please use this identifier to cite or link to this item: `http://hdl.handle.net/2445/35460`
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dc.contributor.advisorOller i Sala, Josep Maria-
dc.contributor.authorCorcuera Valverde, José Manuel-
dc.contributor.otherUniversitat de Barcelona. Departament d'Estadística-
dc.date.accessioned2013-04-23T13:52:11Z-
dc.date.available2013-04-23T13:52:11Z-
dc.date.issued1994-06-14-
dc.identifier.isbn9788469385111-
dc.identifier.urihttp://hdl.handle.net/2445/35460-
dc.description.abstract[eng] The aim of that we shall refer to as "Intrinsic Analysis" of the statistical estimation, is to develop a statistical estimation theory analogous to the classical one, based on geometrical structures of the statistical models. Then one goal of the Intrinsic Analysis is to supply invariant tools in order to analyse the performance of an estimator, and another is to obtain results that are analogous to classical ones and to establish relationships between the classical non invariant measures and the invariant herein obtained. In this thesis, taking into account the Riemannian structure of the regular parametric statistical models, an intrinsic bias measure is obtained by considering the mean value of random manifold-valued maps. The mean square of the Riemannian, or Rao, distance is the invariant analogous to the mean square error. The first part of the thesis is concerned with the moments of a random field on an n-dimensional C-infinity real manifold, and also the mean value concept of a random object which takes values on a (Hausdorff and connected) manifold equipped with an affine connection, through the exponential map. We emphasize the analogies and differences between moments and mean values, and we consider, in particular, the Riemannian case. The second part is the application of these results to the study of some invariant measures analogous to the bias and mean square error corresponding to a statistical estimator. The third and fourth parts are devoted to the development of intrinsic versions of the local and global Cramér-Rao lower bounds. In the fifth part we study the behaviour of the mean square Rao distance of an estimator when it is conditioned by a sufficient statistic, in order to obtain intrinsic versions of the Rao-Blackwell and Lehmann-Scheffée theorems. Finally some asymptotic properties, specially related with the maximum-likelihood estimator, are studied.eng
dc.format.mimetypeapplication/pdf-
dc.language.isospa-
dc.publisherUniversitat de Barcelona-
dc.rights(c) Corcuera Valverde, 1994-
dc.subject.classificationEstimació d'un paràmetre-
dc.subject.otherParameter estimation-
dc.titleAnálisis intrínseco de la estimación puntualspa
dc.typeinfo:eu-repo/semantics/doctoralThesis-
dc.typeinfo:eu-repo/semantics/publishedVersion-
dc.identifier.dlB.45423-2010-
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess-
dc.identifier.tdxhttp://www.tdx.cat/TDX-1015110-123514-
dc.identifier.tdxhttp://hdl.handle.net/10803/1570-
Appears in Collections:Tesis Doctorals - Departament - Estadística

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