A note on model identification and discrimination for simple linear regression.

*(English)*Zbl 1193.62131Summary: The paper considers the issue of designing an experiment to determine which of two competing simple regression models, the linear model MI and the quadratic model MII, better describes the data, first by identifying both models and then by discriminating between them. The discrimination between models is considered by comparing both fitted observations and predicted observations. Two criterion functions \(I\) and \(J\) are proposed. The criterion function \(I\) is completely new. We observe that the celebrated J. Kiefer and J. Wolfowitz design [Ann. Math. Stat. 30, 271–294 (1959; Zbl 0090.11404)] does not perform very well under the proposed new criterion function \(I\). It is shown that the criterion function \(J\) is in fact the criterion function for the Kiefer-Wolfowitz design and therefore it performs the best under \(J\). We also demonstrate that the A. Biswas and P. Chaudhuri sequential designs [Biometrika 89, No. 3, 709–718 (2002; Zbl 1037.62070)] at various stages are in fact designs within a class \(D_1\) considered in this paper. We are therefore able to evaluate the performance of Biswas-Chaudhuri designs with respect to the \(I\) criterion function. We consider another class of designs \(D_2\) and obtain the best design within this class with respect to the \(J\) criterion function.