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Weakly nonlinear regression model with constraints I: nonlinear hypothesis

Lubomír KubácekEva Tesaríková — 2005

Discussiones Mathematicae Probability and Statistics

The problem considered is under which conditions in weakly nonlinear regression model with constraints I a weakly nonlinear hypothesis can be tested by linear methods. The aim of the paper is to find a region around the approximate value of the regression parameter with the following property. If we are certain that the actual value of the regression parameter is in this region, then the linear method of testing can be used without any significant deterioration of the inference.

How to deal with regression models with a weak nonlinearity

Eva TesaríkováLubomír Kubáček — 2001

Discussiones Mathematicae Probability and Statistics

If a nonlinear regression model is linearized in a non-sufficient small neighbourhood of the actual parameter, then all statistical inferences may be deteriorated. Some criteria how to recognize this are already developed. The aim of the paper is to demonstrate the behaviour of the program for utilization of these criteria.

Estimation of dispersion in nonlinear regression models with constraints

Lubomír KubáčekEva Tesaříková — 2004

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Dispersion of measurement results is an important parameter that enables us not only to characterize not only accuracy of measurement but enables us also to construct confidence regions and to test statistical hypotheses. In nonlinear regression model the estimator of dispersion is influenced by a curvature of the manifold of the mean value of the observation vector. The aim of the paper is to find the way how to determine a tolerable level of this curvature.

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