On Exact K-optimal Designs Minimizing the Condition Number

Abstract

A new design criterion based on the condition number of an information matrix is proposed to construct optimal designs for linear models, and the resulting designs are called K-optimal designs. The relationship between exact and asymptotic K-optimal designs is derived. Since it is usually hard to find exact optimal designs analytically, we apply a simulated annealing algorithm to compute K-optimal design points on continuous design spaces. Specific issues are addressed to make the algorithm effective. Through exact designs, we can examine some properties of the K-optimal designs such as symmetry and the number of support points. Examples and results are given for polynomial regression models and linear models for fractional factorial experiments. In addition, K-optimal designs are compared with A-optimal and D-optimal designs for polynomial regression models, showing that K-optimal designs are quite similar to A-optimal designs.

Keywords:

• Annealing algorithm
• Condition number
• Continuous design space
• Fractional factorial design
• Optimal design
• Polynomial regression
• Quadratic model
• Symmetric design

Mathematics Subject Classification:

• Primary 62K05, 62F35
• Secondary 62P12

Notes

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