Optimal Designs for Regression Models With a Constant Coefficient of Variation

Abstract

In this article we consider the problem of constructing optimal designs for models with a constant coefficient of variation. We explore the special structure of the information matrix in these models and derive a characterization of optimal designs in the sense of Kiefer and Wolfowitz (1960) Besides locally optimal designs, Bayesian and standardized minimax optimal designs are also considered. Particular attention is spent on the problem of constructing D-optimal designs. The results are illustrated in several examples where optimal designs are calculated analytically and numerically.

Keywords:

• 62K05

Keywords:

• Optimal design
• Heteroscedasticity
• Constant coefficient of variation
• Polynomial regression

Acknowledgments

The authors are grateful to Martina Stein, who typed parts of this article with considerable technical expertise, and to Tina Kiss and Markus Lange for assistance with the numerical calculations. The work of Holger Dette was supported by the Sonderforschungsbereich 873, Statistik nichtlinearer dynamischer Prozesse (Teilprojekt C2). This collaboration was initiated when both authors were visiting fellows at the Sir-Isaac-Newton-Institute in Cambridge. We gratefully acknowledge their support.