On the equivalence between Stein identity and de Bruijn identity
Additional Document Info
This paper illustrates the equivalence between two fundamental results: Stein identity, originally proposed in the statistical estimation realm, and de Bruijn identity, considered for the first time in the information theory field. Two distinctive extensions of de Bruijn identity are presented as well. For arbitrary but fixed input and noise distributions, the first-order derivative of differential entropy is expressed by means of a function of the posterior mean, while the second-order derivative of differential entropy is manifested in terms of a function of Fisher information. Several applications exemplify the utility of the proposed results. 2012 IEEE.
name of conference
2012 IEEE International Symposium on Information Theory Proceedings