Confidence regions in singular weakly nonlinear regression models with constraints (Q2810991)

The paper deals with the problem of constructing confidence regions for a group of functions of parameters in nonlinear, possibly singular regression models with constraints. The problem is rather complicated, mainly when the number of parameters is large. In principle, if the nonlinearity of the model is weak, then it is possible to approximate the confidence region by a confidence ellipsoid in the linearized model. In the case of nonlinearity and simultaneous singularity of the model, however, the construction of such confidence regions is even more complicated. In this paper, for singular weakly nonlinear models, the author suggests a new procedure based on nonlinearity measures which enable to decide whether the confidence region can be substituted by an approximate ellipsoid constructed in the linearized version of the model, or not. Here, the weakly nonlinear regression models with constraints are considered in two forms, the model with type I constraints and the model with type II constraints, for more details see also [\textit{L. Kubáček}, Math. Slovaca 65, No. 5, 1181--1198, (2015; Zbl 1363.62074)].