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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.
62J02 General nonlinear regression
62F10 Point estimation
62H12 Estimation in multivariate analysis
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