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Optimal designs for quadratic regression with random block effects: the case of block size two. (English) Zbl 1341.62251
Summary: Optimal approximate designs for quadratic regression with random block effects in the case of block size two are considered. We obtain, with respect to the Schur ordering, an essentially complete class consisting of designs with a simple structure. The locally \(D\)- and \(A\)-optimal designs given in [the second author et al., Stat. Sin. 5, No. 2, 485–497 (1995; Zbl 0828.62066); J. Stat. Plann. Inference 77, No. 2, 321–335 (1999; Zbl 0930.62073)] belong to this class. We explicitly identify locally \(E\)-optimal designs and show that for each \(p\), \(-\infty \leq p \leq 1\), there is a unique \(\phi_p\)-design in this class. Bayesian \(\phi_p\)-optimal designs are also considered.
62K05 Optimal statistical designs
62K10 Statistical block designs
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