Abstract #301785

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JSM 2003 Abstract #301785
Activity Number: 375
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #301785
Title: D-optimal Designs for Weighted Polynomial Regression: A Functional-Algebraic Approach
Author(s): Fu-Chuen Chang*+
Companies: National Sun Yat-sen University
Address: Dept. of Applied Math, Kaohsiung 804, , , Taiwan
Keywords: approximate design ; D-optimal ; implicit function theorem ; weighted polynomial regression ; Taylor series ; eigenvalue
Abstract:

This paper is concerned with the problem of computing the $D$-optimal design for polynomial regression with weight function $\omega(x)$ on the interval $[-a,a]$. It is shown that if $\omega'(x)/\omega(x)$ is a rational polynomial and $\omega(0)\neq 0$, the problem of constructing $D$-optimal designs can be transformed into the problem of determining one or more unknown parameters via a differential equation approach. By using Taylor expansion, we provide a recursive algorithm to compute these parameters. Therefore Taylor expansion for the $D$-optimal support points for weighted polynomial regression on a neighborhood of the origin can be determined from the differential equation.

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