Displaying similar documents to “Suitability of linearization of nonlinear problems not only in biology and medicine”

Linearized regression model with constraints of type II

Lubomír Kubáček (2003)

Applications of Mathematics

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A linearization of the nonlinear regression model causes a bias in estimators of model parameters. It can be eliminated, e.g., either by a proper choice of the point where the model is developed into the Taylor series or by quadratic corrections of linear estimators. The aim of the paper is to obtain formulae for biases and variances of estimators in linearized models and also for corrected estimators.

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.

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.