On a global measure of nonlinearity and its application in parameter estimation in nonlinear regression

Abstract

The theoretical and computational challenges in least squares estimationof parameters in nonlinear regression models are well documented in statisticalliterature. The measures of nonlinearity are intended to quantify the degree ofnonlinearity and to explain the relationship between nonlinearity and statisticalproperties of a model. A new measure of nonlinearity reflecting the model’s globalbehavior is introduced and discussed in this paper. Two new criteria for globalminimum of the sum of squares in nonlinear regression incorporating this measureare presented and illustrated on several published examples.