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Objective Bayesian point and region estimation in location-scale models
Bernardo, José M. (Universitat de València)

Data: 2007
Resum: Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this requires the use of an invariant loss function; moreover, an objective solution requires the use of a prior which does not introduce subjective elements. The combined use of an invariant information-theory based loss function, the intrinsic discrepancy, and an objective prior, the reference prior, produces a general solution to both point and region estimation problems. In this paper, estimation of the two parameters of univariate location-scale models is considered in detail from this point of view, with special attention to the normal model. The solutions found are compared with a range of conventional solutions.
Drets: Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. Creative Commons
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Confidence Intervals ; Credible Regions ; Decision Theory ; Intrinsic Discrepancy ; Intrinsic Loss ; Location-Scale Models ; Noninformative Prior ; Reference Analysis ; Region Estimation ; Point Estimation
Publicat a: SORT : statistics and operations research transactions, Vol. 31, Núm. 1 (January-June 2007) , p. 3-44, ISSN 1696-2281

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