Linear-quadratic estimators in a special structure of the linear model. (English) Zbl 0832.62050

Summary: The paper deals with the linear model with uncorrelated observations. The dispersions of the values observed are linear-quadratic functions of the unknown parameters of the mean (measurements by devices of a given class of precision). Investigated are the locally best linear-quadratic unbiased estimators as improvements of locally best linear unbiased estimators in the case that the design matrix has none, one or two linearly dependent rows.


62H12 Estimation in multivariate analysis
62J99 Linear inference, regression
62F10 Point estimation
62F99 Parametric inference
Full Text: EuDML


[1] V. Fajt: Electrical measurements. SNTL/ALFA, Praha, 1978.
[2] Guido del Pino: The unifying role of iterative generalized least squares in statistical algorithms. Statistical Science 4 (1980), 394-408. · Zbl 0955.62607
[3] J. Nelder and R. Wedderburn: Generalized linear models. J. Roy. Statist. Soc. Ser A (1972), 370-384.
[4] C.R. Rao and S.K. Mitra: Generalized Inverse of Matrices and Its Applications. J. Willey, New York, 1971.
[5] K. Rinner and F. Benz: Jordan/Eggert/Kneissl Handbuch der Vermessungskunde. Band VI, Stuttgart, 1966.
[6] R. Wedderburn: Quasi-likelihood functions, generalized linear models and the GaussNewton method. Biometrika 61 (1974), 439-447. · Zbl 0292.62050
[7] G. Wimmer: Linear model with variance depending on the mean value. Mathematica Slovaca 42 (1992), 223-238. · Zbl 0764.62055
[8] G. Wimmer: Estimation in a special structure of the linear model. Mathematica Slovaca 43 (1993), 221-264. · Zbl 0779.62061
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.