Optimal designs for a class of nonlinear regression models

Holger Dette, Viatcheslav B. Melas, Andrey Pepelyshev

The Annals of Statistics · 2004 · Volume 32 · Issue 5

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 f0≡0 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.

Keywords

41A50, 62K05, Chebyshev systems, c-optimal design, E-optimal design, local optimal designs, rational models

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