Robustness of designs for model discrimination

A class of models is considered to describe the data to be collected using a design of experiment. One model within the class will possibly describe the data more adequately than the others which will be the “true model” but we do not know its identification. In the pioneering work of Atkinson and Fedorov (1975) [4,3], the discrimination criterion T optimality was introduced for pairwise discrimination between models with the assumption that one of the models being the true model. The recent papers of Dette and Titoff (2009) [6], Atkinson (2010) [1], Dette, Melas and Shpilev (2012) [5] presented fundamental research on T optimal designs. A large number of other researchers also made major contributions to the area of finding T optimal designs with their references available in the papers mentioned. This paper considers the problem of pairwise discrimination between two competing models when the true model may or may not be one of them. The characterization of robustness of designs are given under the different possible true models within the class of models considered under the proposed J and I optimality criterion functions. The J criterion is in fact equivalent to the T criterion when the true model is indeed one of the two competing models in their pairwise comparison. Illustrative examples are presented for the particular polynomial regression models and optimum designs are also presented for a class of designs D with a special equal replications by considering the Dette–Titoff class and the Dette–Melas–Shpilev representation. The J d and I d optimality criterion functions are also proposed to deal with the unknown model parameters in the J and I optimality criterion functions.