Degeneracy in nonlinear least squares

Abstract

As a result of random and/or systematic errors in the observations nonlinear least squares criteria may become degenerate in the sense that their structure essentially differs from that in the errorless case. The paper studies this degeneracy for models described by linear combinations of functions belonging to the same nonlinearly parametric family. For these models elementary types of degeneracy are theoretically explained and illustrated in a number of numerical examples. For practice, the most important conclusion is that degeneracy may preclude the computation of parameter values in the correct model structure.