Results in the Theory and Construction of D -Optimum Experimental Designs

Henry P. Wynn

247 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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

Abstract

Summary A method of generating D-optimum design measures as defined by Kiefer and Wolfowitz is briefly described. The relevant theorem is generalized to yield a method of generating D8-optimum design measures for a specific subset of s of the parameters in the regression model. The one parameter case is described in further detail. An analogous theorem for discrete designs with a fixed number of points is proved giving a lower bound to the optimality achievable with such designs. A final section is devoted to the loss in efficiency entailed by almost equal replication of a given discrete design. The discussion is extended to the one-dimensional polynomial model and the optimality of the replication is conjectured for the general case and proved for the quadratic case.

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References

1959Optimum Experimental Designs 1959Optimum Designs in Regression Problems 1970The Sequential Generation of $D$-Optimum Experimental Designs 1966Optimal Experimental Designs 1958On the Nonrandomized Optimality and Randomized Nonoptimality of Symmetrical Designs 1961Optimum Designs in Regression Problems, II

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1982RESPONSE SURFACE EXPERIMENTATION 1982Branch-and-Bound Search for Experimental Designs Based onDOptimality and Other Criteria 2000Optimization Problems and Methods in Quality Control and Improvement 1974Planning Experiments for Discriminating between Models 2016I-Optimal Design of Mixture Experiments 1975Optimal Design: Some Geometrical Aspects of D-Optimality 1983Some Guidelines for Constructing ExactD-Optimal Designs on Convex Design Spaces 2010Monotonic convergence of a general algorithm for computing optimal designs

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