6533b7cffe1ef96bd12595d6
RESEARCH PRODUCT
Objective Bayesian point and region estimation in location-scale models.
José Miguel Bernardosubject
Intrinsic LossTeoria de la decisióRegion Estimation:62 Statistics::62B Sufficiency and information [Classificació AMS]Intrinsic DiscrepancyStatisticsEstadísticaReference Analysis:MATEMÁTICAS::Estadística [UNESCO]UNESCO::MATEMÁTICAS::EstadísticaCredible RegionsConfidence Intervals ; Credible Regions ; Decision Theory ; Intrinsic Discrepancy ; Intrinsic Loss ; Location-Scale Models ; Noninformative Prior ; Reference Analysis ; Region Estimation ; Point EstimationPoint EstimationDecision TheoryInferenceInferència:62 Statistics::62F Parametric inference [Classificació AMS]Confidence IntervalsLocation-Scale ModelsNoninformative Prior:62 Statistics::62C Decision theory [Classificació AMS]description
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. Jose.M.Bernardo@uv.es
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-01-01 |