Linear-quadratic estimators in a special structure of the linear model

Gejza Wimmer

Applications of Mathematics (1995)

  • Volume: 40, Issue: 2, page 81-105
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Wimmer, Gejza. "Linear-quadratic estimators in a special structure of the linear model." Applications of Mathematics 40.2 (1995): 81-105. <http://eudml.org/doc/32907>.

@article{Wimmer1995,
abstract = {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.},
author = {Wimmer, Gejza},
journal = {Applications of Mathematics},
keywords = {parametric estimation; linear model with variances depending on the mean value parameters; locally best linear-quadratic unbiased estimator (LBLQUE); variances depending on the mean value parameters; linear model; uncorrelated observations; locally best linear-quadratic unbiased estimators; locally best linear unbiased estimators},
language = {eng},
number = {2},
pages = {81-105},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear-quadratic estimators in a special structure of the linear model},
url = {http://eudml.org/doc/32907},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Wimmer, Gejza
TI - Linear-quadratic estimators in a special structure of the linear model
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 2
SP - 81
EP - 105
AB - 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.
LA - eng
KW - parametric estimation; linear model with variances depending on the mean value parameters; locally best linear-quadratic unbiased estimator (LBLQUE); variances depending on the mean value parameters; linear model; uncorrelated observations; locally best linear-quadratic unbiased estimators; locally best linear unbiased estimators
UR - http://eudml.org/doc/32907
ER -

References

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  1. Electrical measurements, SNTL/ALFA, Praha, 1978. (Czech) (1978) 
  2. The unifying role of iterative generalized least squares in statistical algorithms, Statistical Science 4 (1980), 394–408. (1980) MR1041764
  3. Generalized linear models, J. Roy. Statist. Soc. Ser A (1972), 370–384. (1972) 
  4. Generalized Inverse of Matrices and Its Applications, J. Willey, New York, 1971. (1971) MR0338013
  5. Jordan/Eggert/Kneissl Handbuch der Vermessungskunde, Band VI, Stuttgart, 1966. (1966) 
  6. Quasi-likelihood functions, generalized linear models and the GaussNewton method, Biometrika 61 (1974), 439–447. (1974) MR0375592
  7. Linear model with variance depending on the mean value, Mathematica Slovaca 42 (1992), 223–238. (1992) MR1170107
  8. Estimation in a special structure of the linear model, Mathematica Slovaca 43 (1993), 221–264. (1993) Zbl0779.62061MR1274604

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