On the equivalence between Stein and de Bruijn identities

Details On the equivalence between Stein and de Bruijn identities On the equivalence between Stein and de Bruijn identities

2012-01-31

arxiv.org/abs/1202.0015v2

Computer Science

Information Theory

This paper has been withdrawn by the author due to some reasons

Scientific paper

This paper focuses on proving the equivalence between Stein's identity and de Bruijn's identity. Given some conditions, we prove that Stein's identity is equivalent to de Bruijn's identity. In addition, some extensions of de Bruijn's identity are presented. For arbitrary but fixed input and noise distributions, there exist relations between the first derivative of the differential entropy and the posterior mean. Moreover, the second derivative of the differential entropy is related to the Fisher information for arbitrary input and noise distributions. Several applications are presented to support the usefulness of the developed results in this paper.

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