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

Abstract

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.

Keywords:

• A-Equivalence Theorem
• A-optimal design
• Implicit function theorem
• Recursive algorithm
• Remez's exchange procedure
• Taylor expansion
• Weighted polynomial regression

Mathematics Subject Classification:

• Primary 62K05

Acknowledgments

This research was supported by the National Science Council of the Republic of China (Grant No. 93-2118-M-110-005-). The author is indebted to two referees for their constructive comments and suggestions on an earlier version of this article.