Nonlinear regression

Summary

Nonlinear regression fits a model in which the mean response is a nonlinear function of the unknown parameters. Examples are an exponential decay or a growth curve. The parameters are usually estimated by nonlinear least squares, which has no closed formula and is solved by iterative methods such as Gauss–Newton or Levenberg–Marquardt. Inference relies on a linear approximation of the model near the estimate, so it is approximate and asymptotic. It is the natural tool when a scientific theory dictates the form of the mean function.