Optimal Designs for Rational Regression Models
In this article, we consider locally optimal designs problems for rational regression models. In the case where the degrees of polynomials in the numerator and denominator differ by at most 1, we identify an invariance property of the optimal designs if the denominator polynomial is palindromic, which reduces the optimization problem by 50%. The results clarify and extend the particular structure of locally c-, D-, and E-optimal designs for inverse quadratic regression models that have been found by Haines (1992) and have recently been extended by Dette and Kiss (2009). We also investigate the relation between the D-optimal designs for the Michaelis-Menten and EMAX models from a more general point of view. The results are illustrated by several examples.
KeywordsRational regression models Optimal designs Chebyshev systems Palindromic polynomials
AMS Subject Classification62K05
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