D-optimal designs via a cocktail algorithm

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Optimal Experimental Design Methods Advanced Statistical Methods and Models Statistical and numerical algorithms

Abstract

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This cocktail algorithm extends the well-known vertex direction method (VDM; Fedorov in Theory of Optimal Experiments, 1972 ) and the multiplicative algorithm (Silvey et al. in Commun. Stat. Theory Methods 14:1379–1389, 1978 ), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.

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References

2007Optimum Experimental Designs, with SAS 1974General Equivalence Theory for Optimum Designs (Approximate Theory)1972Results in the Theory and Construction of D -Optimum Experimental Designs 1978An algorithm for optimal designs on a design space 1993Optimum Experimental Designs for Properties of a Compartmental Model 2010Monotonic convergence of a general algorithm for computing optimal designs 1978Some Algorithmic Aspects of the Theory of Optimal Designs

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