Open Access
December, 1991 Bayesian Optimal Designs for Linear Regression Models
Sadi M. El-Krunz, W. J. Studden
Ann. Statist. 19(4): 2183-2208 (December, 1991). DOI: 10.1214/aos/1176348392


A Bayesian version of Elfving's theorem is given for the $\mathbf{c}$-optimality criterion with emphasis on the inherent geometry. Conditions under which a one-point design is Bayesian $\mathbf{c}$-optimum are described. The class of prior precision matrices $R$ for which the Bayesian $\mathbf{c}$-optimal designs are supported by the points of the classical $\mathbf{c}$-optimal design is characterized. It is proved that the Bayesian $\mathbf{c}$-optimal design, for large $n,$ is always supported by the same support points as the classical one if the number of support points and the number of regression functions are equal. Examples and a matrix analog are discussed.


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Sadi M. El-Krunz. W. J. Studden. "Bayesian Optimal Designs for Linear Regression Models." Ann. Statist. 19 (4) 2183 - 2208, December, 1991.


Published: December, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0755.62056
MathSciNet: MR1135170
Digital Object Identifier: 10.1214/aos/1176348392

Primary: 62K05
Secondary: 62J05

Keywords: Bayesian $\mathbf{c}$-optimality , Elfving's theorem

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1991
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