Une étude algébrique de l’admissibilité en estimation linéaire de la moyenne sur un modéle général de Gauss-Markov

• Autorzy: Téchené Jean-Jacques
• Języki publikacji: FR

Abstrakty

EN

It would appear useful to come back to the question of admissibility in linear estimation on a general Gauss-Markov model. We prove how a functional approach to this problem, based on a very important LaMotte theorem [11], clearly leads to characterization of all admissible linear estimators of mean vector or linear transformation of mean vector. Thus we have managed to modify significantly a Klonecki and Zontek theorem [9] allowing us to find in a different way an essential characterization shown by Baksalary and Markiewicz [4], based on the logic put forward by Rao (cf. [13] and [14]). We also give a variational characterization of admissibility in linear estimation and a geometrical proof of a Baksalary and Mathew theorem [7] relative to equality between the set of best linear unbiased estimators (or Gauss-Markov estimators) and the set of linear admissible estimators of mean vector. We finish by explaining more results on admissibility of linear estimators of vector parameters.

Słowa kluczowe

EN

Gauss-Markov model; linear estimation; La Motte theorem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 2
• Strony: 219--245
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Téchené Jean-Jacques

• Departement de Mathématiques – Recherche, I.P.R.A. - Université de Pau et des Pays de l’Adour, Avenue de l’Université - 64000 Pau, France

Bibliografia

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• [4] — Admissible linear estimators in the general Gauss-Markov model, ibidem 19 (1988), pp. 349-359.
• [5] — A matrix inequality and admissibility of linear estimators with respect to mean square error matrix criterion, Linear Algebra Appl. 112 (1989), pp. 9-18.
• [6] — Admissible linear estimators of an arbitrary vector of parametric functions in the general Gauss-Markov model, J. Statist. Plann. Inference 26 (1990), pp. 161-171.
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• [9] — and S. Zontek, On the structure of admissible linear estimators, J. Multivariate Anal. 24 (1988), pp. 11-30.
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