A Note on Criterion-Robust Optimal Designs for Model Discrimination and Parameter Estimation in Polynomial Regression Models

Abstract

Consider the problem of discriminating between the polynomial regression models on [−1, 1] and estimating parameters in the models. Zen and Tsai (2002) proposed a multiple-objective optimality criterion, M _γ-criterion, which uses weight γ (0 ≤ γ ≤ 1) for model discrimination and α = β = (1 − γ)/2 for parameter estimation in each model. In this article, we generalize it to a wider setup with different values of α and β. For instance, α = 2 β suggests that the “smaller” model is more likely to be the true model. Using similar techniques, the corresponding criterion-robust optimal design is investigated. A study for the original criterion-robust optimal design with α = β, through M-efficiency, shows that it is good enough for any wider setup.

Keywords:

• Canonical moments
• Efficiency
• M _{γ m *}-optimal design
• Multiple-objective
• Selection criterion

Mathematics Subject Classification:

• 62K05

Acknowledgments

The authors would like to thank the referees for their helpful comments; this research was partially supported by NSC93-2118-M006-004 from the National Science Council, R.O.C.