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November, 1976 Remez's Procedure for Finding Optimal Designs
William J. Studden, Jia-Yeong Tsay
Ann. Statist. 4(6): 1271-1279 (November, 1976). DOI: 10.1214/aos/1176343659

Abstract

The Remez exchange procedures of approximation theory are used to find the optimal design for the problem of estimating $c'\theta$ in the regression model $EY(x) = \theta_1f_1(x) + \theta_2f_2(x) + \cdots + \theta_kf_k(x)$, when $c$ is not a linear combination of less than $k$ vectors of the form $f(x)$. A geometric approach is given first with a proof of convergence. When the design space is a closed interval, the Remez exchange procedure is illustrated by two examples. This type procedure can be used to find the optimal design very efficiently, if there exists an optimal design with $k$ support points.

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William J. Studden. Jia-Yeong Tsay. "Remez's Procedure for Finding Optimal Designs." Ann. Statist. 4 (6) 1271 - 1279, November, 1976. https://doi.org/10.1214/aos/1176343659

Information

Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0347.62057
MathSciNet: MR418354
Digital Object Identifier: 10.1214/aos/1176343659

Subjects:
Primary: 62K05

Keywords: information matrix , optimal design , regression functions , Remez exchange procedures

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • November, 1976
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