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July, 1981 Some Classes of Optimality Criteria and Optimal Designs for Complete Two-Way Layouts
N. Gaffke
Ann. Statist. 9(4): 893-898 (July, 1981). DOI: 10.1214/aos/1176345530

Abstract

For a given class of linear models in standard form an optimal experimental design is to be chosen for estimating some linear functions of the unknown parameters. An optimality criterion is defined to be a real function of the covariance matrices of the Gauss-Markov estimators. Conditions which are imposed on the criteria are monotonicity, quasiconvexity or quasiconcavity, and invariance or order-invariance. A characterization of the $D$-criterion by order-invariance is included which strengthens a result of P. Whittle. In the main part of the paper optimal designs for the usual two-way layouts in ANOVA are computed for large classes of optimality criteria. Some related optimization problems are solved with the technique of majorization of vectors in the sense of Schur.

Citation

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N. Gaffke. "Some Classes of Optimality Criteria and Optimal Designs for Complete Two-Way Layouts." Ann. Statist. 9 (4) 893 - 898, July, 1981. https://doi.org/10.1214/aos/1176345530

Information

Published: July, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0468.62072
MathSciNet: MR619293
Digital Object Identifier: 10.1214/aos/1176345530

Subjects:
Primary: 62K05
Secondary: 90C10

Keywords: BLUE , linear model , majorization , optimal design , two-way layout

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • July, 1981
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