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On formulas for the distribution of nonlinear L. S. estimates. (English) Zbl 0633.62056

A nonlinear regression model with the least squares (L.S.) estimator of a vector of parameters is considered. The relation between the density of the L.S. estimator and its approximation is shown. If a linear approximation of the nonlinear regression is used, the approximate density is the density of the linear L.S. estimates.
The approximate density can be expressed using the terms of the expected information and of the conditional information. The case of \(cov(y,y)=\sigma^ 2K\) is also studied. K is a known positive definite matrix. The approximate density is considered also in terms of the asymptotical theory of S. Amari (e.g. \(\alpha\)-affine connections).
Reviewer: P.Froněk

MSC:

62J02 General nonlinear regression
62F10 Point estimation
62E15 Exact distribution theory in statistics
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[1] DOI: 10.1093/biomet/70.2.343 · Zbl 0532.62006 · doi:10.1093/biomet/70.2.343
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