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Certain Inequalities in Information Theory and the Cramer-Rao Inequality
The Annals of Mathematical Statistics
Vol. 25, No. 4 (Dec., 1954), pp. 745-751
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2236658
Page Count: 7
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The Cramer-Rao inequality provides, under certain regularity conditions, a lower bound for the variance of an estimator , . Various generalizations, extensions and improvements in the bound have been made, by Barankin , , Bhattacharyya , Chapman and Robbins , Fraser and Guttman , Kiefer , and Wolfowitz , among others. Further considerations of certain inequality properties of a measure of information, discussed by Kullback and Leibler , 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.
The Annals of Mathematical Statistics © 1954 Institute of Mathematical Statistics