Abstract:

The non-linear regression model $y = \eta (\vartheta ) + \varepsilon $ with an error vector $\varepsilon $ having the zero mean and the covariance matrix $\delta^{2}I$ $(\delta^{2}$ unknown) is considered. Some sufficient conditions of 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's and G. A. Milliken's research [1] concerning local reparameterization of a singular model onto a regular model.