The Annals of Statistics

Accounting for Intrinsic Nonlinearity in Nonlinear Regression Parameter Inference Regions

David C. Hamilton, Donald G. Watts, and Douglas M. Bates

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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.

Article information

Ann. Statist., Volume 10, Number 2 (1982), 386-393.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62J02: General nonlinear regression
Secondary: 62F25: Tolerance and confidence regions

Intrinsic curvature nonlinear regression approximate inference regions


Hamilton, David C.; Watts, Donald G.; Bates, Douglas M. Accounting for Intrinsic Nonlinearity in Nonlinear Regression Parameter Inference Regions. Ann. Statist. 10 (1982), no. 2, 386--393. doi:10.1214/aos/1176345780.

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