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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.

On admissibility in estimating the mean squared error of a linear estimator

Stępniak Czesław

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 1

33--38

Consider a linear estimator of a parametric vector Cß in the normal Gauss-Markov model Y ~ N {Xß, σV). The Mean Squared Error of such an estimator may be presented in the form kσ+ß' X' KXß and may be estimated by quadratics in Y Some basic decision-theoretic questions in the estimation are discussed. Among others, some admissible estimators of the MSE in several classes of the quadratics are given.