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Certain Inequalities in Information Theory and the Cramer-Rao Inequality

S. Kullback
The Annals of Mathematical Statistics
Vol. 25, No. 4 (Dec., 1954), pp. 745-751
Stable URL: http://www.jstor.org/stable/2236658
Page Count: 7
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Certain Inequalities in Information Theory and the Cramer-Rao Inequality
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Abstract

The Cramer-Rao inequality provides, under certain regularity conditions, a lower bound for the variance of an estimator [7], [15]. Various generalizations, extensions and improvements in the bound have been made, by Barankin [1], [2], Bhattacharyya [3], Chapman and Robbins [5], Fraser and Guttman [11], Kiefer [12], and Wolfowitz [16], among others. Further considerations of certain inequality properties of a measure of information, discussed by Kullback and Leibler [14], yields a greater lower bound for the information measure (formula (4.11)), and leads to a result which may be considered a generalization of the Cramer-Rao inequality, the latter following as a special case. The results are used to define discrimination efficiency and estimation efficiency at a point in parameter space.

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