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Statistica Sinica 8(1998), 467-476



Gunseog Kang and John O. Rawlings

Soongsil University, Korea and North Carolina State University

Abstract: The marginal curvature by Clarke (1987) for individual parameters in nonlinear models not only improves the inference on each parameter but also has been found useful in experimental design for nonlinear models. In this article we develop the marginal curvature for functions of parameters. We show that, for a given reparametrization, the marginal curvatures for the transformed parameters can be computed without determining the inverse transformation. Furthermore, the marginal curvature for a function of parameters depends only on the marginal curvatures of the original parameters and on the derivatives of the function with respect to the parameters involved in that function.

We also present a more efficient computing algorithm of Clarke's marginal curvature measure. The resulting expression enables us to compare Clarke's measure with other available measures.

Key words and phrases: Experimental design, linear approximation, parameter-effects curvature, parameter transformation.

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