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2 Probability and Mathematical Statistics

2 1998

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

Téchené Jean-Jacques

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 2

219--245

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.

Quelques propriétés extrémales des valeurs singuliéres d’un operateur compact et leurs applications aux analyses factorielles d’une probabilité ou d’une fonction aléatoire. II: D’analyses factorielles linéaires d’une probabilité ou d’une fonction aléatoire

Pousse Alain, Téchené Jean-Jacques

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 1

1--18

This paper extends the work by Rao [6] concerning factor analysis criteria equivalent to the principal component analysis of a finite set of random variables. We search for global (i.e. non-iterative) criteria for the factor analysis of a probability defined on a separable Hilbert space or of a real random function other than a finite or countable set of real random variables. We compare this analysis with principal component analysis defined in a general probabilistic setting by Dauxois and Pousse [2].