Cook, R. Dennis; Goldberg, Miriam L. Curvatures for parameter subsets in nonlinear regression. (English) Zbl 0651.62060 Ann. Stat. 14, 1399-1418 (1986). 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. Cited in 6 Documents MSC: 62J02 General nonlinear regression 62F25 Parametric tolerance and confidence regions Keywords:relative curvature measures of nonlinearity; normal, nonlinear regression model; linearization-based approximate confidence intervals; Bates-Watts measures; likelihood function; intrinsic curvature; parameter-effects curvature array Citations:Zbl 0455.62028 × Cite Format Result Cite Review PDF Full Text: DOI