Open Access
June, 1982 Accounting for Intrinsic Nonlinearity in Nonlinear Regression Parameter Inference Regions
David C. Hamilton, Donald G. Watts, Douglas M. Bates
Ann. Statist. 10(2): 386-393 (June, 1982). DOI: 10.1214/aos/1176345780


Joint confidence and likelihood regions for the parameters in nonlinear regression models can be defined using the geometric concepts of sample space and solution locus. Using a quadratic approximation to the solution locus, instead of the usual linear approximation, it is shown that these inference regions correspond to ellipsoids on the tangent plane at the least squares point. Accurate approximate inference regions can be obtained by mapping these ellipsoids into the parameter space, and measures of the effect of intrinsic nonlinearity on inference can be based on the difference between the tangent plane ellipsoids and the sphere which would be obtained using a linear approximation.


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David C. Hamilton. Donald G. Watts. Douglas M. Bates. "Accounting for Intrinsic Nonlinearity in Nonlinear Regression Parameter Inference Regions." Ann. Statist. 10 (2) 386 - 393, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0537.62045
MathSciNet: MR653514
Digital Object Identifier: 10.1214/aos/1176345780

Primary: 62J02
Secondary: 62F25

Keywords: approximate inference regions , Intrinsic curvature , Nonlinear regression

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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