S-plus tools for model selection in nonlinear regression (Q1297853)

The aim of this paper is to present the computational tools written in S-plus for the simultaneous selection of parametric nonlinear regression and variance models from a rather rich model class. The selection procedure starts with a list of competitive models \(f_m(x,\theta)\), \(m=1,\dots,M\), of regression functions from which one (or several) appropriate candidates are to be chosen by minimization of the cross-validation criterion taking into account one of the following objectives: estimation of unknown regression functions, prediction of future values of the response variables, calibration or estimation of certain parameters useful in applications. S-plus tools allow to handle such steps: description of data and classes of reasonable regression models; generating of initial parameter estimates; selection of the best model. The procedure also includes the choice of a Box-Cox transformation which can improve the fit of a model, the assessment of the accuracy of estimates in chosen models by a moment oriented bootstrap method, construction of confidence, prediction and calibration intervals, and standardized presentation of the results at each stage of the analysis. A numerical example illustrates the performance of the proposed methodology.