On the equivalence between Stein and de Bruijn identities
Information Theory
2012-07-24 v4 math.IT
Abstract
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.
Cite
@article{arxiv.1202.0015,
title = {On the equivalence between Stein and de Bruijn identities},
author = {Sangwoo Park and Erchin Serpedin and Khalid Qaraqe},
journal= {arXiv preprint arXiv:1202.0015},
year = {2012}
}
Comments
This is the final version, which was accepted in IEEE trans. on Information Theory