Model Selection, Transformations and Variance Estimation in Nonlinear Regression

The results of analyzing experimental data using a parametric approach may heavily depend on the chosen model. In this paper we propose procedures for the adequate selection of nonlinear regression models if the intended use of the model is among the following: 1. prediction of future values of the response variable, 2. estimation of the unknown regression function, 3. calibration or 4. estimation of some parameter with a certain meaning in the corresponding field of application. Moreover, we propose procedures for variance modelling and for selecting an appropriate nonlinear transformation of the observations which may lead to an improved accuracy. We show how to assess the accuracy of the parameter estimators by a "moment oriented bootstrap procedure". This procedure may also be used for the construction of confidence, prediction and calibration intervals. Programs written in Splus which realize our strategy for nonlinear regression modelling and parameter estimation are described as..