Statistica Sinica 21 (2011), 1557-1570
doi:10.5705/ss.2009.202

OPTIMAL DESIGNS FOR ESTIMATING THE DERIVATIVE

IN NONLINEAR REGRESSION

Holger Dette$^1$, Viatcheslav B. Melas$^2$ and Petr Shpilev$^2$

$^1$Ruhr-Universität Bochum and $^2$St. Petersburg State University

Abstract: We consider the problem of estimating the derivative of the expected response in nonlinear regression models. It is demonstrated that in many cases the optimal designs for estimating the derivative have either on $m$ or $m-1$ support points, where $m$ denotes the number of unknown parameters in the model. It is also shown that the support points and weights of the optimal designs are analytic functions, and this result is used to construct a numerical procedure for the calculation of the optimal designs. The results are illustrated in exponential regression and rational regression models.

Key words and phrases: Chebyshev system, c-optimal designs, implicit function theorem, nonlinear regression.