D-optimal designs via a cocktail algorithm

Details D-optimal designs via a cocktail algorithm D-optimal designs via a cocktail algorithm

2009-10-31

arxiv.org/abs/0911.0108v3

Statistics and Computing 21 (2011) 475-481

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A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanat

Scientific paper

10.1007/s11222-010-9183-2

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 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 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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