Bad luck in quadratic improvement of the linear estimator in a special linear model

Gejza Wimmer

Applications of Mathematics (1998)

  • Volume: 43, Issue: 1, page 1-7
  • ISSN: 0862-7940

Abstract

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The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.

How to cite

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Wimmer, Gejza. "Bad luck in quadratic improvement of the linear estimator in a special linear model." Applications of Mathematics 43.1 (1998): 1-7. <http://eudml.org/doc/32993>.

@article{Wimmer1998,
abstract = {The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.},
author = {Wimmer, Gejza},
journal = {Applications of Mathematics},
keywords = {linear model with dispersions depending on the mean value parameters; locally best linear-quadratic unbiased estimator (LBLQUE) of mean value parameters; dispersions depending on mean value parameters; locally best linear-quadratic unbiased estimators; mean value estimation; linear models},
language = {eng},
number = {1},
pages = {1-7},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bad luck in quadratic improvement of the linear estimator in a special linear model},
url = {http://eudml.org/doc/32993},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Wimmer, Gejza
TI - Bad luck in quadratic improvement of the linear estimator in a special linear model
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 1
SP - 1
EP - 7
AB - The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.
LA - eng
KW - linear model with dispersions depending on the mean value parameters; locally best linear-quadratic unbiased estimator (LBLQUE) of mean value parameters; dispersions depending on mean value parameters; locally best linear-quadratic unbiased estimators; mean value estimation; linear models
UR - http://eudml.org/doc/32993
ER -

References

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  1. Foundations of Estimation Theory, Elsevier, Amsterdam, 1988. (1988) MR0995671
  2. Generalized Inverse of Matrices and Its Applications, J. Wiley, New York, 1971. (1971) MR0338013
  3. Jordan/Eggert/Kneissl Handbuch der Vermessungskunde, Band VI, Stuttgart, 1966. (1966) 
  4. Linear model with variances depending on the mean value, Mathematica Slovaca 42 (1992), 223–238. (1992) Zbl0764.62055MR1170107
  5. Uniformly best linear-quadratic estimator in a special structure of the regression model, Acta Math. Univ. Comenianae LXI (1992), 243–250. (1992) Zbl0819.62061MR1205877
  6. Estimation in a special structure of the linear model, Mathematica Slovaca 43 (1993), 221–264. (1993) Zbl0779.62061MR1274604
  7. Linear-quadratic estimators in a special structure of the linear model, Applications of Mathematics 40 (1995), 81–105. (1995) Zbl0832.62050MR1314481
  8. Covariance matrix elements estimation: Special linear model without and with repeated measurement, Mathematica Slovaca 47 (1997), . (1997) MR1796337

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