Curvatures for Parameter Subsets in Nonlinear Regression
R. Dennis Cook, Miriam L. Goldberg
The Annals of Statistics · 1986 · Volume 14 · Issue 4
Abstract
The relative curvature measures of nonlinearity proposed by Bates and Watts (1980) 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.
Keywords
62F25, 62J02, Confidence regions, curvature measures, Fieller-Creasy problem, least squares, likelihood
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