Tests in weakly nonlinear regression model

Lubomír Kubáček; Eva Tesaříková

Displaying similar documents to “Tests in weakly nonlinear regression model”

Underparametrization of weakly nonlinear regression models

Lubomír Kubáček, Eva Tesaříková (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A large number of parameters in regression models can be serious obstacle for processing and interpretation of experimental data. One way how to overcome it is an elimination of some parameters. In some cases it need not deteriorate statistical properties of estimators of useful parameters and can help to interpret them. The problem is to find conditions which enable us to decide whether such favourable situation occurs.

Linearization regions for a confidence ellipsoid in singular nonlinear regression models

Lubomír Kubáček, Eva Tesaříková (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A construction of confidence regions in nonlinear regression models is difficult mainly in the case that the dimension of an estimated vector parameter is large. A singularity is also a problem. Therefore some simple approximation of an exact confidence region is welcome. The aim of the paper is to give a small modification of a confidence ellipsoid constructed in a linearized model which is sufficient under some conditions for an approximation of the exact confidence region. ...

Linearization regions for confidence ellipsoids

Lubomír Kubáček, Eva Tesaříková (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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If an observation vector in a nonlinear regression model is normally distributed, then an algorithm for a determination of the exact $(1 - α)$ -confidence region for the parameter of the mean value of the observation vector is well known. However its numerical realization is tedious and therefore it is of some interest to find some condition which enables us to construct this region in a simpler way.

Weakly nonlinear regression model with constraints I: nonlinear hypothesis

Lubomír Kubácek, Eva Tesaríková (2005)

Discussiones Mathematicae Probability and Statistics

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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. ...