A proof of the Fisher information inequality via a data processing argument Export

@article{citeulike:333455, abstract = {The Fisher information J(X) of a random variable X under a translation parameter appears in information theory in the classical proof of the entropy-power inequality (EPI). It enters the proof of the EPI via the De-Bruijn identity, where it measures the variation of the differential entropy under a Gaussian perturbation, and via the convolution inequality J(X+Y)^-1\⩾J(X)^-1+J(Y) ^-1 (for independent X and Y), known as the Fisher information inequality (FII). The FII is proved in the literature directly, in a rather involved way. We give an alternative derivation of the FII, as a simple consequence of a \“data processing inequality\” for the Cramer-Rao lower bound on parameter estimation}, author = {Zamir, R.}, citeulike-article-id = {333455}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/18.669301}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=669301}, doi = {10.1109/18.669301}, journal = {Information Theory, IEEE Transactions on}, keywords = {estimation, fisher-information}, number = {3}, pages = {1246--1250}, posted-at = {2005-09-28 06:27:36}, priority = {2}, title = {A proof of the Fisher information inequality via a data processing argument}, url = {http://dx.doi.org/10.1109/18.669301}, volume = {44}, year = {1998} }

TY - JOUR ID - citeulike:333455 L3 - citeulike-article-id:333455 N2 - The Fisher information J(X) of a random variable X under a translation parameter appears in information theory in the classical proof of the entropy-power inequality (EPI). It enters the proof of the EPI via the De-Bruijn identity, where it measures the variation of the differential entropy under a Gaussian perturbation, and via the convolution inequality J(X+Y)^-1⩾J(X)^-1+J(Y) ^-1 (for independent X and Y), known as the Fisher information inequality (FII). The FII is proved in the literature directly, in a rather involved way. We give an alternative derivation of the FII, as a simple consequence of a “data processing inequality” for the Cramer-Rao lower bound on parameter estimation IS - 3 JF - Information Theory, IEEE Transactions on EP - 1250 TI - A proof of the Fisher information inequality via a data processing argument VL - 44 SP - 1246 KW - estimation KW - fisher-information AU - Zamir, R PY - 1998/// UR - http://dx.doi.org/10.1109/18.669301 ER -