Fitting Segmented Polynomial Regression Models Whose Join Points Have to Be Estimated

Abstract The study considers the problem of finding the least squares estimates for the unknown parameters of a regression model which consists of grafted polynomial submodels. The abscissae of the join points are a subset of the unknown parameters. Examples are given to illustrate how continuity and differentiability conditions on the model can be used to reparameterize the model so as to allow Modified Gauss-Newton fitting. A slightly generalized version of Hartley's theorem is stated to extend the Modified Gauss-Newton method to this problem.