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

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-criterion, which uses weight (01) for model discrimination and ==(1-)/2 for parameter estimation in each model. In this article, we generalize it to a wider setup with different values of and . For instance, =2 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 =, through M-efficiency, shows that it is good enough for any wider setup.