parametric estimation; linear model with variances depending on the mean value parameters; locally best linear-quadratic unbiased estimator (LBLQUE)
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.
 V. Fajt: Electrical measurements. SNTL/ALFA, Praha, 1978. (Czech)
 Guido del Pino: The unifying role of iterative generalized least squares in statistical algorithms
. Statistical Science 4 (1980), 394–408. MR 1041764
 J. Nelder and R. Wedderburn: Generalized linear models. J. Roy. Statist. Soc. Ser A (1972), 370–384.
 C.R. Rao and S.K. Mitra: Generalized Inverse of Matrices and Its Applications
. J. Willey, New York, 1971. MR 0338013
 K. Rinner and F. Benz: Jordan/Eggert/Kneissl Handbuch der Vermessungskunde. Band VI, Stuttgart, 1966.
 R. Wedderburn: Quasi-likelihood functions, generalized linear models and the GaussNewton method
. Biometrika 61 (1974), 439–447. MR 0375592
 G. Wimmer: Linear model with variance depending on the mean value
. Mathematica Slovaca 42 (1992), 223–238. MR 1170107
 G. Wimmer: Estimation in a special structure of the linear model
. Mathematica Slovaca 43 (1993), 221–264. MR 1274604
| Zbl 0779.62061