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On estimable and locally-estimable functions in the non-linear regression model. (English) Zbl 0766.62038
Summary: The nonlinear regression model $$y=\eta(\vartheta)+\varepsilon$$ with an error vector $$\varepsilon$$ having zero mean and covariance matrix $$\delta^ 2I$$ $$(\delta^ 2$$ unknown) is considered. Some sufficient conditions for estimability and local estimability of the function of the parameter $$\vartheta$$ are obtained, whilst the regularity of the model (i.e. the regularity of Jacobi matrix of the function $$\eta(\vartheta))$$ is not required. Consequently, there are given — in addition — precisions of A. H. Bird and G. A. Milliken’s research [Commun. Stat., Theory Methods 5, 999-1012 (1976)] concerning local reparameterization of singular models to regular models.
##### MSC:
 62J02 General nonlinear regression 62F10 Point estimation 62H12 Estimation in multivariate analysis
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##### References:
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