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- W1601496069 abstract "Publisher Summary This chapter focuses on approximate linear regression design. It provides an overview of the invariance and admissibility of designs, their interrelations and their implications to design optimality, including numerical algorithms. Invariance structures combined with results on admissibility provide a tool to attack optimal design problems of high dimensions, as occurring for second and third order multiple polynomial models. Invariance with respect to infinite (though compact) transformation and matrix groups usually calls for the Haar probability measures, involving deep measure theoretic results. The Karlin–Studden necessary condition on the support of an admissible design is known to become useless for regression models involving a constant term. Well known numerical algorithms for solving extremum problems in optimal design are pure gradient methods, among them the steepest descent method of Fedorov and Wynn. However, after a quick but rough approximation towards the optimum they become very inefficient. The Quasi–Newton methods of Gaffke and Heiligers provide an efficient way of computing the optimum very accurately." @default.
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- W1601496069 date "1996-01-01" @default.
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- W1601496069 title "30 Approximate designs for polynomial regression: Invariance, admissibility, and optimality" @default.
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- W1601496069 doi "https://doi.org/10.1016/s0169-7161(96)13032-7" @default.
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