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Loss Functions in Restricted Parameter Spaces and Their Bayesian Applications

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Loss Functions in Restricted Parameter Spaces and Their Bayesian Applications. / Mozgunov, Pavel; Jaki, Thomas Friedrich; Gasparini, Mauro.

In: Journal of Applied Statistics, Vol. 46, No. 13, 03.10.2019, p. 2314-2337.

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Mozgunov, Pavel ; Jaki, Thomas Friedrich ; Gasparini, Mauro. / Loss Functions in Restricted Parameter Spaces and Their Bayesian Applications. In: Journal of Applied Statistics. 2019 ; Vol. 46, No. 13. pp. 2314-2337.

Bibtex

@article{991fd8b738dd437ba64435566e3a8e0c,
title = "Loss Functions in Restricted Parameter Spaces and Their Bayesian Applications",
abstract = "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.",
keywords = "Aitchison distance, Bayesian estimation, Scale parameter",
author = "Pavel Mozgunov and Jaki, {Thomas Friedrich} and Mauro Gasparini",
year = "2019",
month = oct,
day = "3",
doi = "10.1080/02664763.2019.1586848",
language = "English",
volume = "46",
pages = "2314--2337",
journal = "Journal of Applied Statistics",
issn = "0266-4763",
publisher = "Routledge",
number = "13",

}

RIS

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 -