Pázman, A. On formulas for the distribution of nonlinear L. S. estimates. (English) Zbl 0633.62056 Statistics 18, 3-15 (1987). 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 Cited in 2 ReviewsCited in 7 Documents MSC: 62J02 General nonlinear regression 62F10 Point estimation 62E15 Exact distribution theory in statistics Keywords:differential geometry; density of estimates; least squares; linear approximation of the nonlinear regression; approximate density; expected information; conditional information; asymptotical theory of S. Amari; affine connections PDFBibTeX XMLCite \textit{A. Pázman}, Statistics 18, 3--15 (1987; Zbl 0633.62056) Full Text: DOI References: [1] DOI: 10.1093/biomet/70.2.343 · Zbl 0532.62006 · doi:10.1093/biomet/70.2.343 [2] FIEDLER M., Special Matrices and Their Use in Numerical Mathematics. (Czech.) (1981) [3] GANTMACHER F.R., Matrix Theory (Russian) (1966) [4] IVANOV A.V., Math. Operationsf. Statist. 14 pp 7– (1983) [5] PÁZMAN A., Math. Operationsf. Statist 15 pp 323– (1984) [6] PÁZMAN A., Kybernetika (prague) 20 pp 209– (1984) [7] PINCUS R., Math. Operationsf. Statist 15 pp 37– (1984) [8] STERNBERG S., Lectures on Differential Geometry 2 (1965) · Zbl 0129.13102 [9] AMARI SHUN-ICHI, Differential-Geometrical Methods in Statistics 28 (1985) · Zbl 0559.62001 · doi:10.1007/978-1-4612-5056-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.