Monotonicity of Entropy and Fisher Information: A Quick Proof via Maximal Correlation
arXiv:1610.04174
Abstract
A simple proof is given for the monotonicity of entropy and Fisher information associated to sums of i.i.d. random variables. The proof relies on a characterization of maximal correlation for partial sums due to Dembo, Kagan and Shepp.
To appear, Communications on Information and Systems