×

zbMATH — the first resource for mathematics

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.
MSC:
62J02 General nonlinear regression
62F10 Point estimation
62H12 Estimation in multivariate analysis
PDF BibTeX XML Cite
Full Text: EuDML Link
References:
[1] A. H. Bird, G. A. Milliken: Eastimable functions in the non-linear model. Com. Statist. Theory Methods 5 (1976, 11, 999 - 1012. · Zbl 0341.62055
[2] J. Dieudonne: Treatise on Analysis. Volume III. Academic Press, New York 1972. · Zbl 0268.58001
[3] M. Golubickij, V. Gijemin: Ustojčivije otobraženija i jich osoběnnosti. Mir, Moskva 1974.
[4] V. Jarník: Diferenciální počet II (Differential Calculus). NČSAV, Praha 1956.
[5] H. Kohoutková: Exponential regression. Fasciculi Mathematici Nr. 20 (1989), 111 - 116.
[6] A. Pázman: Nonlinear least squares - uniqueness versus ambiguity. Math. Operationsforsch. Statist., Ser. Statist. 15 (1984), 323 - 336. · Zbl 0562.62053
[7] R. C. Rao: Lineární metody statistické indukce a jejich aplikace (Linear Methods of Statistical Induction and their Applications). Academia, Praha 1978.
[8] V. I. Smirnov: Kurs vysšej matematiki IV (A Course of Higher Mathematics). Gos. izd. tech.-teor. literatury, Moskva 1953.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.