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Some inequalities related to the Stam inequality

Abram KaganTinghui Yu — 2008

Applications of Mathematics

Zamir showed in 1998 that the Stam classical inequality for the Fisher information (about a location parameter) 1 / I ( X + Y ) 1 / I ( X ) + 1 / I ( Y ) for independent random variables X , Y is a simple corollary of basic properties of the Fisher information (monotonicity, additivity and a reparametrization formula). The idea of his proof works for a special case of a general (not necessarily location) parameter. Stam type inequalities are obtained for the Fisher information in a multivariate observation depending on a univariate location...

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