Estimating a restricted normal mean

Kumar, Somesh; Tripathi, Yogesh Mani

doi:10.1007/s00184-007-0157-0

Cited by 4 publications

(1 citation statement)

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“…We consider the function L (2) sq given in (17) to obtain Bayes estimators. As the loss function (17) is the sum of the univariate precautionary loss functions (2), the following estimators are usedα i = E(α 2 i ), i = 1, 2 where the expectation E is taken with respect to the posterior distribution.…”

Section: Bayesian Estimation Of the Parameters Of A Gamma Distributionmentioning

confidence: 99%

Loss functions in restricted parameter spaces and their Bayesian applications

Mozgunov

Jaki

Gasparini

2019

Journal of Applied Statistics

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Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined on a restricted space. It can also be an inappropriate choice in the context when an extreme overestimation and/or underestimation results in severe consequences and a more conservative estimator is preferred. We advocate a class of loss functions for parameters defined on restricted spaces which infinitely penalize boundary decisions like the squared error loss does on the real line. We also recall several properties of loss functions such as symmetry, convexity and invariance. We propose generalizations of the squared error loss function for parameters defined on the positive real line and on an interval. We provide explicit solutions for corresponding Bayes estimators and discuss multivariate extensions. Four well-known Bayesian estimation problems are used to demonstrate inferential benefits the novel Bayes estimators can provide in the context of restricted estimation.

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Section: Bayesian Estimation Of the Parameters Of A Gamma Distributionmentioning

confidence: 99%