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Curvatures for parameter subsets in nonlinear regression. (English) Zbl 0651.62060

The relative curvature measures of nonlinearity proposed by D. M. Bates and D. G. Watts [J. R. Stat. Soc., Ser. B 42, 1-25 (1980; Zbl 0455.62028)] are extended to an arbitrary subset of the parameters in a normal, nonlinear regression model. In particular, the subset curvatures proposed indicate the validity of linearization-based approximate confidence intervals for single parameters. The derivation produces the original Bates-Watts measures directly from the likelihood function. When the intrinsic curvature is negligible, the Bates-Watts parameter-effects curvature array contains all information necessary to construct curvature measures for parameter subsets.

MSC:

62J02 General nonlinear regression
62F25 Parametric tolerance and confidence regions

Citations:

Zbl 0455.62028
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