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

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1 Author(s)
Zamir, R. ; Dept. of Electr. Eng. Syst., Tel Aviv Univ., Israel

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

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 3 )