(in Theory and Methods)
Fitting Segmented Polynomial Regression Models Whose
Join Points have to be Estimated
A. R. Gallant, Wayne A. Fuller
Journal of the American Statistical Association, Vol. 68,
No. 341. (Mar., 1973), pp. 144-147.
AbstractThe 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.