Abstract
In the usual linear regression model we investigate the geometric structure of a class of minimax optimality criteria containing Elfving's minimax and Kiefer's $\phi_p$-criteria as special cases. It is shown that the optimal designs with respect to these criteria are also optimal for $A'\theta$, where $A$ is any inball vector (in an appropriate norm) of a generalized Elfving set. The results explain the particular role of the $A$- and $E$-optimality criterion and are applied for determining the optimal design with respect to Elfving's minimax criterion in polynomial regression up to degree 9.
Citation
H. Dette. B. Heiligers. W. J. Studden. "Minimax Designs in Linear Regression Models." Ann. Statist. 23 (1) 30 - 40, February, 1995. https://doi.org/10.1214/aos/1176324453
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