On Fisher Information Inequalities and Score Functions in Non-invertible Linear Systems

Volume 4, Issue 4, 2003

Article 71

ON FISHER INFORMATION INEQUALITIES AND SCORE FUNCTIONS IN NON-INVERTIBLE LINEAR SYSTEMS

C. VIGNAT AND J.-F. BERCHER

E.E.C.S. UNIVERSITY OF MICHIGAN
1301 N. BEAL AVENUE
ANN ARBOR MI 48109, USA.
E-Mail: vignat@univ-mlv.frURL: http://www-syscom.univ-mlv.fr/~vignat/

ÉQUIPE SIGNAL ET INFORMATION
ESIEE AND UMLV
93 162 NOISY-LE-GRAND, FRANCE.
E-Mail: jf.bercher@esiee.fr

Received 04 June, 2003; Accepted 09 September, 2003.
Communicated by: F. Hansen

ABSTRACT. In this note, we review score functions properties and discuss inequalities on the Fisher Information Matrix of a random vector subjected to linear non-invertible transformations. We give alternate derivations of results previously published in [6] and provide new interpretations of the cases of equality.

[6] R. ZAMIR, A proof of the Fisher information matrix inequality via a data processing argument, IEEE Trans. on Information Theory, IT, 44(3) (1998), 1246-1250.

Key words:
Fisher information, Non-invertible linear systems.

2000 Mathematics Subject Classification:
62B10, 93C05, 94A17.

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