Computing A-optimal Designs for Weighted Polynomial Regression by Taylor Expansion

This article is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m - a, m + a], m, a > 0. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points, and weights are analytic functions of a at a = 0. We make use of a Taylor expansion to provide a recursive procedure for calculating the A-optimal designs. Examples are presented to illustrate the procedures for computing the optimal designs.