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Small-sample distributional properties of nonlinear regression estimators (a geometric approach). (English) Zbl 0724.62063

The author’s paper is an invited paper with seven contributions to the discussion on the application of differential methods in nonlinear regression. It is mainly a survey of the topic how to approximate the density of the least squares estimator in nonlinear regression.
A short presentation of the geometry of the model is given. In the model with Gaussian errors the asymptotic normal approximation, the second order Edgeworth expansion and the saddlepoint approximation are compared. Further, the author presents the possibility of improving the approximation in the non-Gaussian model.
Reviewer: S.Zwanzig (Berlin)

MSC:

62J02 General nonlinear regression
62E20 Asymptotic distribution theory in statistics
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