Accuracy of linear approximation for fitted values in nonlinear regression

Abstract

Bates and Watts (1981) have discussed the problems of reparameterizing nonlinear models in obtaining accurate linear approximation confidence regions for the parameters. A similar problem exists with computing confidence curves for fitted values or predictions. The statistical behavior of fitted values does not depend on the parameterization. Thus, as long as the intrinsic curvature is small, standard Wald intervalsfor fitted values are likely to be sufficient. Accuracy of linear approximation for fitted values is investigated using confidence curves.