The Non-Uniqueness of Some Designs for Discriminating Between Two Polynomial Models in One Variable
T-optimum designs for discriminating between two nested polynomial regression models in one variable that differ in the presence or absence of the two highest order terms are studied as a function of the values of the parameters of the true model. For the value of the parameters corresponding to the absence of the next-highest order term, the optimum designs are not unique and can contain an additional support point. A numerical exploration of the non-uniqueness reveals a connection with Ds-optimality for models which do contain the next highest term. Brief comments are given on the analysis of data from such designs
KeywordsOptimum Design Polynomial Model Support Point Royal Statistical Society Design Region
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I am most grateful to a referee who suggested exploring the properties of designs for discriminating between the pairs of models (8) and so led me to the results reported in §4.
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