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Author
Grzybowski Andrzej (Politechnika Częstochowska)
Title
Minimaksowo-odporna estymacja parametrów regresji
Minimax-Robust Estimation of Regression Parameters
Source
Przegląd Statystyczny, 1997, vol. 44, z. 3, s. 427-435, bibliogr. 14 poz.
Statistical Review
Keyword
Regresja liniowa, Estymacja, Optymalizacja decyzji
Linear regression, Estimation, Decision optimization
Note
summ.
Abstract
The problem of minimax-robust linear regression estimation is considered under the assumption that prior knowledge about the regression parameter is available for the decision-maker. The prior knowledge is represented by a given class of probability distributions of the unknown parameter. It is also assumed that a covariance matrix of observations is unknown but belongs to a given set of matrices. Some general results are obtained fot the problem under arbitrary quadratic loss. (original abstract)
Accessibility
The Main Library of the Cracow University of Economics
The Library of Warsaw School of Economics
The Library of University of Economics in Katowice
The Main Library of Poznań University of Economics and Business
The Main Library of the Wroclaw University of Economics
Bibliography
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  1. Bartosiewicz J., Wykłady ze Statystyki Matematycznej, PWN, Warszawa 1989.
  2. Berger J., A robust generalized bayes estimator and confidence region for a multivariate normal mean, Ann. Statist 8 (1980), s. 716-761.
  3. Berger J., Selecting a minimax estimator of a multivariete normal mean, Ann. Statist. 10 (1982), s. 81-92.
  4. Berger J., Robust Bayesian analysis: sensitivity to the prior, J. Statist. Plann. Inference 25 (1990), s. 303-328.
  5. Berger J., Chen S.Y., Minimaxity of empirical Bayes estimators derived from subjective hyperpriors. Advances in Multivariete Statistical Analysis, 1-12, Ed. A.K. Gupta, Riedel Publ. Comp. (1987), s. 1-12.
  6. Ferguson T.S., Mathematical Statistics - a decision theoretic approach, Academic Press, New York, 1967.
  7. Grzybowski A., Minimax control of a system with actuation errors, Applicationes Mathematicae 21, 1 (1991), s. 235-252.
  8. Grzybowski A., Minimax state estimation for stochastic systems with an uncertain parameter, Applicationes Mathematicae 21, 2 (1991), s. 33-42.
  9. Läuter H., A minimax linear estimator for linear parameters under restrictions inform of inequalities, Math. Oper. Stat. 6 (1975), s. 689-695.
  10. Moreno E., Cano J.A., Robust Bayesian analysis with e-contaminations partialy known, J. Roy. Statist. Soc. Ser. B 53-1 (1991), s. 143-155.
  11. Pilz J., Minimax linear regression estimation with symetrie parameter restictions, J. Statist. Plann. Inference 13 (1986), s. 297-318.
  12. Pinelis I.F., O minimaksnom ocenivanii regressii, Teorija Verojatnostej i ee primenenija, 35(3) (1991), s. 494-505.
  13. Rao C.R., Modele liniowe statystyki matematycznej, PWN, Warszawa 1982.
  14. Verdu S., Poor H.V., On minimax robustness: A general approach and applications, IEEE Trans. Inform. Theory IT-30 (1984), s. 328-340.
Cited by
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ISSN
0033-2372
Language
pol
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