Optimal designs for a class of nonlinear regression models

Details Optimal designs for a class of nonlinear regression models Optimal designs for a class of nonlinear regression models

2005-03-29

arxiv.org/abs/math/0503677v1

Annals of Statistics 2004, Vol. 32, No. 5, 2142-2167

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000382 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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 f_0\equiv 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.

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