Linearized models with constraints of type I.
The author considers the nonlinear regression model \[ \mathbf Y\sim \mathcal N \big (\mathbf f(\mathbf \beta ),\,\mathbf \Sigma \big ), \] where the value of the vector parameter \(\mathbf \beta \) is unknown and constrained by a nonlinear condition \(\big \{\mathbf \beta \: g(\beta )=\mathbf 0\big \}\), where \(g(\cdot )\) is a function with continuous second derivatives. The main aim is to show how to proceed in estimation of parameters when either the linearized or quadratic approximation of the model is used. Of big practical interest are the simple but practically usable rules how to proceed in such a case.
nonlinear regression model with constraints
scientific article; zbMATH DE number 5074678