Confidence regions for parameter subsets in nonlinear regression

Abstract

Confidence regions for some of the parameters in nonlinear regression models are often based on the large sample distribution of the least squares estimator, or equivalently a linear approximation to the model. These regions have a simple ellipsoidal shape but their nominal level is often misleading. Confidence regions based on the likelihood ratio and on the scores are examined and geometric interpretations are given. A simple method of approximating both types of confidence regions is derived, which uses second derivatives of the model to account for intrinsic and parameter effects nonlinearity.