Objective Bayesian point and region estimation in location-scale models
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 t...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2099/3807 |
| Acceso en línea: | https://hdl.handle.net/2099/3807 |
| Access Level: | acceso abierto |
| Palabra clave: | Statistics Decision theory Inference Estadística Teoria de la decisió Inferència Classificació AMS::62 Statistics::62B Sufficiency and information Classificació AMS::62 Statistics::62C Decision theory Classificació AMS::62 Statistics::62F Parametric inference |
| Sumario: | 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. |
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