Optimal Experimental Designs in Two Dimensions Using Minimum Bias Estimation

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Abstract
The general problem of minimum bias estimation is reviewed for polynomial response surface models, where the true model, a polynomial of degree d + k — 1, is estimated by a polynomial of degree d — 1. Through the choice of estimator, the same minimum integrated squared bias B is achieved for any experimental design that satisfies a simple estimability condition. This design flexibility is used to construct D-optimal, V-optimal, and A-optimal experimental designs in two dimensions through a computerized simplex search procedure. The resulting optimal designs for both square and circular regions of interest are discussed and recommendations as to their use are made.

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