Zur Quantifizierung und Analyse der Nichtlineariät von Regressionsmodellen

In nonlinear regression statistical analysis based upon interpretation of the parameter estimates may be quite different from linear regression. An important point is that for finite samples the least squares estimator (LSE) is not unbiased. nor is it a minimum variance estimator: for nonlinear models, the LSE has these properties under some assumptions only asymptotically and many statistical conclusions are based upon this asymptotic theorie. But there are a lot of nonlinear models where the asymptotic properties are poorly approximated for finite samples. Assessing the nonlinearity can show us if statistical tests the justification of which rests on the assumption of linearity are valid. Better parameterizations and experimental design are good possibilities to reduce the non-neglible nonlinearitv of certain models. A case study shows that experimental design can reduce the nonlinearity considerably. (author's abstract)