# A matrix inequality and admissibility of linear estimators with respect to the mean square error matrix criterion

- Authors
- Journal
- Linear Algebra and its Applications 0024-3795
- Publisher
- Elsevier
- Publication Date
- Volume
- 112
- Identifiers
- DOI: 10.1016/0024-3795(89)90584-3

## Abstract

Abstract Given matrices A, B and vectors a, b, a necessary and sufficient condition is established for the Löwner partial ordering ( Am+ a)( Am+ a)′ ⩽ ( Bm+ b)( Bm+ b)′ to hold for all vectors m. This result is then applied to derive a complete characterization of estimators that are admissible for a given vector of parametric functions among the set of all linear estimators under the general Gauss-Markov model, when the mean square error matrix is adopted as the criterion for evaluating the estimators.

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