Optimal Design: Some Geometrical Aspects of D-Optimality

D. Michael Titterington

117 citations0/0 files storedBiometrika

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Optimal Experimental Design Methods Advanced Optimization Algorithms Research Advanced Statistical Methods and Models

Abstract

SUMMARY The duality relationships between D-type optimal designs and problems of covering a subset of Euclidean space by central ellipsoids and ellipsoidal cylinders are described and consequences that aid the solution of either problem are discussed. It is shown that there are also design duals for the problems of finding minimal covering spheres and ellipsoids or cylinders whose centres or axes are chosen optimally.

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References

1972Theory of optimal experiments 1952Optimum Allocation in Linear Regression Theory 1972Results in the Theory and Construction of D -Optimum Experimental Designs

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1980On linear regression designs which maximize information 2001One hundred years of the design of experiments on and off the pages of Biometrika 2008Improving updating rules in multiplicative algorithms for computing D-optimal designs 2018A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments 1976Convergent Design Sequences, for Sufficiently Regular Optimality Criteria 2006Improvements on removing nonoptimal support points in -optimum design algorithms

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