The Annals of Statistics

Optimal designs for a class of nonlinear regression models

Holger Dette, Viatcheslav B. Melas, and Andrey Pepelyshev

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 32, Number 5 (2004), 2142-2167.

Dates
First available in Project Euclid: 27 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1098883785

Digital Object Identifier
doi:10.1214/009053604000000382

Mathematical Reviews number (MathSciNet)
MR2102506

Zentralblatt MATH identifier
1056.62084

Subjects
Primary: 62K05: Optimal designs 41A50: Best approximation, Chebyshev systems

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

Citation

Dette, Holger; Melas, Viatcheslav B.; Pepelyshev, Andrey. Optimal designs for a class of nonlinear regression models. Ann. Statist. 32 (2004), no. 5, 2142--2167. doi:10.1214/009053604000000382. https://projecteuclid.org/euclid.aos/1098883785


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