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Computing A-optimal Designs for Weighted Polynomial Regression by Taylor Expansion
Authors:Fu-Chuen Chang  Yang-Chan Su
Institution:1. Department of Applied Mathematics , National Sun Yat-sen University , Taiwan, ROC fuchuen@gmail.com;3. Trade-van Information Services CO. , Taiwan, ROC
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
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