Splus Tools for Model Selection in Nonlinear Regression

The results of analyzing experimental data using a parametric approach may heavily depend on the chosen model. With this paper we describe computational tools in Splus for a simultaneous selection of parametric regression and variance models from a relatively rich model class and of Box-Cox variable transformations by minimisation of a cross-validation criterion. For this we use modifications of the standard cross-validation criterion adapted to each of the following objectives: 1. Estimation of the unknown regression function, 2. Prediction of future values of the response variable, 3. Calibration or 4. Estimation of some parameter with a certain meaning in the corresponding field of application. We describe how the accuracy of parameter estimators is assessed by a "moment oriented bootstrap procedure". This new procedure and its refinement by a bootstrap based pivot ("double bootstrap") is also used for the construction of confidence, prediction and calibration intervals. The use of our tools is illustrated by an example