zbMATH — the first resource for mathematics

Bad luck in quadratic improvement of the linear estimator in a special linear model. (English) Zbl 0937.62069
The paper concludes the author’s investigations in searching for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in the normal linear model. For the simple linear regression model, where the dispersions of the observed quantities depend on the mean value parameters, there exists no linear-quadratic improvement of the linear estimator of mean value parameters.
Reviewer: K.Zvára (Praha)
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
62F10 Point estimation
Full Text: DOI EuDML
[1] Kubáček L.: Foundations of Estimation Theory. Elsevier, Amsterdam, 1988.
[2] Rao C.R. and Mitra S.K.: Generalized Inverse of Matrices and Its Applications. J. Wiley, New York, 1971. · Zbl 0236.15004
[3] Rinner K., Benz F.: Jordan/Eggert/Kneissl Handbuch der Vermessungskunde. Band VI, Stuttgart, 1966.
[4] Wimmer G.: Linear model with variances depending on the mean value. Mathematica Slovaca 42 (1992), 223-238. · Zbl 0764.62055
[5] Wimmer G.: Uniformly best linear-quadratic estimator in a special structure of the regression model. Acta Math. Univ. Comenianae LXI (1992), 243-250. · Zbl 0819.62061
[6] Wimmer G.: Estimation in a special structure of the linear model. Mathematica Slovaca 43 (1993), 221-264. · Zbl 0779.62061
[7] Wimmer G.: Linear-quadratic estimators in a special structure of the linear model. Applications of Mathematics 40 (1995), 81-105. · Zbl 0832.62050
[8] Wimmer G.: Covariance matrix elements estimation: Special linear model without and with repeated measurement. Mathematica Slovaca 47 (1997), . · Zbl 1053.62542
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.