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August 2001 Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies
Holger Dette, Tobias Franke
Ann. Statist. 29(4): 1024-1049 (August 2001). DOI: 10.1214/aos/1013699990

Abstract

In the common polynomial regression of degree m we determine the design which maximizes the minimum of the $D$-efficiency in the model of degree $m$ and the $D_1$-efficiencies in the models of degree $m-j,\dots, m +k$ ($j, k\ge 0$ given). The resulting designs allow an efficient estimation of the parameters in the chosen regression and have reasonable efficiencies for checking the goodness-of-fit of the assumed model of degree $m$ by testing the highest coefficients in the polynomials of degree $m-j,\dots, m +k$ .

Our approach is based on a combination of the theory of canonical moments and general equivalence theory for minimax optimality criteria. The optimal designs can be explicitly characterized by evaluating certain associated orthogonal polynomials.

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Holger Dette. Tobias Franke. "Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies." Ann. Statist. 29 (4) 1024 - 1049, August 2001. https://doi.org/10.1214/aos/1013699990

Information

Published: August 2001
First available in Project Euclid: 14 February 2002

zbMATH: 1012.62080
MathSciNet: MR1869237
Digital Object Identifier: 10.1214/aos/1013699990

Subjects:
Primary: 33C45 , 62K05

Keywords: associated orthogonal polynomials , D_1-optimality , D-optimality , Minimax optimal designs , robust design , t-test,

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 4 • August 2001
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