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2008 On the frequentist coverage of Bayesian credible intervals for lower bounded means
Éric Marchand, William E. Strawderman, Keven Bosa, Aziz Lmoudden
Electron. J. Statist. 2: 1028-1042 (2008). DOI: 10.1214/08-EJS292

Abstract

For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the 100(1α)% Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space. Various new properties are obtained. Namely, we identify precisely where the minimum coverage is obtained and we show that this minimum coverage is bounded between $1-\frac{3\alpha}{2}$ and $1-\frac{3\alpha}{2}+\frac{\alpha^{2}}{1+\alpha}$; with the lower bound $1-\frac{3\alpha}{2}$ improving (for α1/3) on the previously established ([9]; [8]) lower bound $\frac{1-\alpha}{1+\alpha}$. Several illustrative examples are given.

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Éric Marchand. William E. Strawderman. Keven Bosa. Aziz Lmoudden. "On the frequentist coverage of Bayesian credible intervals for lower bounded means." Electron. J. Statist. 2 1028 - 1042, 2008. https://doi.org/10.1214/08-EJS292

Information

Published: 2008
First available in Project Euclid: 13 November 2008

zbMATH: 1320.62040
MathSciNet: MR2460856
Digital Object Identifier: 10.1214/08-EJS292

Subjects:
Primary: 35Q15 , 42A99 , 45B05 , 62C10 , 62C15 , 62F10 , 62F30

Keywords: Bayesian credible sets , confidence intervals , frequentist coverage probability , logconcavity , restricted parameter space

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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