# Objective Bayesian point and region estimation in location-scale models.

SORT (2007)

• Volume: 31, Issue: 1, page 3-44
• ISSN: 1696-2281

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## Abstract

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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.

## How to cite

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Bernardo, José M.. "Objective Bayesian point and region estimation in location-scale models.." SORT 31.1 (2007): 3-44. <http://eudml.org/doc/41934>.

@article{Bernardo2007,
abstract = {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.},
author = {Bernardo, José M.},
journal = {SORT},
keywords = {Inferencia paramétrica; Inferencia bayesiana; Estimador puntual; Intervalo de confianza; Decisión bayesiana; Estimación por intervalos; confidence intervals; credible regions; decision theory; intrinsic discrepancy; intrinsic loss; location-scale models; noninformative prior; reference analysis; region estimation; point estimation},
language = {eng},
number = {1},
pages = {3-44},
title = {Objective Bayesian point and region estimation in location-scale models.},
url = {http://eudml.org/doc/41934},
volume = {31},
year = {2007},
}

TY - JOUR
AU - Bernardo, José M.
TI - Objective Bayesian point and region estimation in location-scale models.
JO - SORT
PY - 2007
VL - 31
IS - 1
SP - 3
EP - 44
AB - 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.
LA - eng
KW - Inferencia paramétrica; Inferencia bayesiana; Estimador puntual; Intervalo de confianza; Decisión bayesiana; Estimación por intervalos; confidence intervals; credible regions; decision theory; intrinsic discrepancy; intrinsic loss; location-scale models; noninformative prior; reference analysis; region estimation; point estimation
UR - http://eudml.org/doc/41934
ER -

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