Fisher Information Matrix

Let  be a random vector in  and let  be a probability distribution on  with continuous first and second order partial derivatives. The Fisher information matrix of  is the  matrix  whose th entry is given by

			(1)
			(2)

REFERENCES:

Papathanasiou, V. "Some Characteristic Properties of the Fisher Information Matrix via Cacoullos-Type Inequalities." J. Multivariate Analysis 14, 256-265, 1993.

Vignat, C. and Bercher, J.-F. "On Fisher Information Inequalities and Score Functions in Non-Invertible Linear Systems." J. Ineq. Pure Appl. Math. 4, Article 71, 1-9, 2003. https://jipam.vu.edu.au/article.php?sid=312.

Zamir, R. "A Proof of the Fisher Information Matrix Inequality Via a Data Processing Argument." IEEE Trans. Information Th. 44, 1246-1250, 1998.

Zamir, R. "A Necessary and Sufficient Condition for Equality in the Matrix Fisher Information Inequality." Technical Report, Tel Aviv University, Dept. Elec. Eng. Syst., 1997. https://www.eng.tau.ac.il/~zamir/techreport/crb.ps.gz.