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Weakly nonlinear regression model with constraints I: nonlinear hypothesis

Lubomír KubácekEva 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.

How to deal with regression models with a weak nonlinearity

Eva TesaríkováLubomír Kubáček — 2001

Discussiones Mathematicae Probability and Statistics

If a nonlinear regression model is linearized in a non-sufficient small neighbourhood of the actual parameter, then all statistical inferences may be deteriorated. Some criteria how to recognize this are already developed. The aim of the paper is to demonstrate the behaviour of the program for utilization of these criteria.

Variance components and nonlinearity

Lubomír KubáčekEva Tesaříková — 2006

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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. The aim of the...

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