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Weak nonlinearity in a model which arises from the Helmert transformation

Jan Ševčík (2003)

Applications of Mathematics

Nowadays, the algorithm most frequently used for determination of the estimators of parameters which define a transformation between two coordinate systems (in this case the Helmert transformation) is derived under one unreal assumption of errorless measurement in the first system. As it is practically impossible to ensure errorless measurements, we can hardly believe that the results of this algorithm are “optimal”. In 1998, Kubáček and Kubáčková proposed an algorithm which takes errors in both...

Weak nonlinearity of growth curve models

Lubomír Kubáček (2002)

Mathematica Slovaca

Weak pointwise consistency of the cross validatory window estimate in non parametric regression estimation

Gérard Collomb, Pascal Sarda, Philippe Vieu (1985)

Commentationes Mathematicae Universitatis Carolinae

Weakly nonlinear constraints in regression models

Lubomír Kubáček, Eva Tesaříková (2002)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Weakly nonlinear regression model with constraints I: nonlinear hypothesis

Lubomír Kubácek, Eva 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.