Displaying similar documents to “Linearization regions for confidence ellipsoids”

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. ...

Suitability of linearization of nonlinear problems not only in biology and medicine

Jana Vrbková (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion...

Variance components and nonlinearity

Lubomír Kubáček, Eva Tesaříková (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model....