The nonlinear regression model with N observations yi = η(xi,θ) + ϵi, and with the parameter θ subject to q nonlinear constraints Cj(θ) = 0; j = 1,...,q, is considered. As an example, the spline regression with unknown nodes is taken. Expressions for the variances (variance matrices) of the LSE are discussed. Because of the complexity of these expressions, and the singularity of the variance matrix of the LSE for θ, the optimality criteria and their properties, in particular the convexity and the equivalence theorem, are considered from different aspects. Also the possibility of restriction to designs with limited values of measures of nonlinearity is mentioned.
