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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Loss Functions in Restricted Parameter Spaces and Their Bayesian Applications
AU - Mozgunov, Pavel
AU - Jaki, Thomas Friedrich
AU - Gasparini, Mauro
PY - 2019/10/3
Y1 - 2019/10/3
N2 - 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 suboptimal 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.
AB - 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 suboptimal 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.
KW - Aitchison distance
KW - Bayesian estimation
KW - Scale parameter
U2 - 10.1080/02664763.2019.1586848
DO - 10.1080/02664763.2019.1586848
M3 - Journal article
VL - 46
SP - 2314
EP - 2337
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
SN - 0266-4763
IS - 13
ER -