Analytical Properties of Locally D-optimal Designs for Rational Models

The paper is devoted to studying locally D-optimal designs for rational regression models. He et al. (1997) have shown that the problem considered is equivalent to that of D-optimal designs for polynomial regression with polynomial variance function. Both problems were studied in a number of papers with the help of two usual approaches: numerical construction of optimal designs and constructing the designs in a closed analytical form. It appears that the latter form is available only in some special cases. Here another approach is developed. Points of optimal designs are studied as functions of the parameters. It turns out that these functions can be expanded in Taylor series. An example of such expansion for a model with six parameters is given.