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

摘要

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 = 2β 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.