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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.
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.
If an observation vector in a nonlinear regression model is normally distributed, then an algorithm for a determination of the exact -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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