UNE ÉTUDE ALGÉBRIQUE DE L’ADMISSIBILITÉ EN ESTIMATION
LINÉAIRE DE LA MOYENNE SUR UN MODÈLE GÉNÉRAL DE
GAUSS-MARKOV

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -