Isobestic points: Sensitiveness and linearization. (English) Zbl 1065.62118

Kubáček, Lubomír; Fišerová, Eva

Tatra Mt. Math. Publ. 26, No. 2, 217-226 (2003).

The authors investigate the problem of sensitiveness and/or insensitiveness of (weakly) nonlinear regression models with constraints to the perturbations of the parameters of the covariance matrix around the (unknown) true parameters. Moreover, the authors also investigate the effect of linearization of the nonlinear model on the basis of the estimator of the regression parameters. As a special case of a nonlinear regression model with constraints, the authors consider the problem of determination of the isobestic points, known from analytical chemistry.
The paper refers to previously published results of the authors. An important part of the paper is the numerical example with determination of the isobestic point of three lines measured by three independent measuring devices with possibly different precision, including the analysis of the insensitivity regions and the linearization regions, respectively.

Reviewer: Viktor Witkovský (Bratislava )

MSC:

62J02	General nonlinear regression
62F30	Parametric inference under constraints
62J05	Linear regression; mixed models

Keywords:

isobestic points; regression model with constraints; weak nonlinearity; sensitiveness