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October 2004 Optimal designs for a class of nonlinear regression models
Holger Dette, Viatcheslav B. Melas, Andrey Pepelyshev
Ann. Statist. 32(5): 2142-2167 (October 2004). DOI: 10.1214/009053604000000382


For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrema of the equi-oscillating best approximation of the function f00 by a normalized linear combination of the regression functions in the corresponding linearized model. The class of models includes rational, logistic and exponential models and for the rational regression models the E- and c-optimal design problem is solved explicitly in many cases.


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Holger Dette. Viatcheslav B. Melas. Andrey Pepelyshev. "Optimal designs for a class of nonlinear regression models." Ann. Statist. 32 (5) 2142 - 2167, October 2004.


Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62084
MathSciNet: MR2102506
Digital Object Identifier: 10.1214/009053604000000382

Primary: 41A50 , 62K05

Keywords: Chebyshev systems , c-optimal design , E-optimal design , local optimal designs , rational models

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 5 • October 2004
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