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Linear comparative calibration with correlated measurements

Gejza Wimmer, Viktor Witkovský (2007)

Kybernetika

The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the...

Linearization regions for a confidence ellipsoid in singular nonlinear regression models

Lubomír Kubáček, Eva Tesaříková (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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

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.

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