Uniqueness of surfaces and global identifiability in nonlinear regression models

Abstract

The parameter of a nonlinear regression model is determined uniquely for al¬most all experimental designs if the number of experimental points is greater than the dimension of the parameter and different regression functions have no weak contact of infi¬nite order. This result yields global identifiability for most practically used curve-fitting models, especially with polynomial, exponential and trigonometric regression functions. In this approach regression models with errors of measurement in the independent variables are included as well. The main theorem does not belong to statistics. It established the geometric fact that parameter-dependent C∞-surfaces are almost surely determined uniquely by sufficiently many base points. The proof shows that the singular zeros of spares C∞-mappings can be imbedded in a countale union of C∞-manifolds with a sufficiently small dimension provided the coordinate functions have no weak contact of infinits order for different parameters.