Curvatures for parameter subsets in nonlinear regression (Q1106592)

The relative curvature measures of nonlinearity proposed by \textit{D. M. Bates} and \textit{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.