Generalized Entropy Power Inequalities and Monotonicity Properties of Information
arXiv:cs/0605047 · doi:10.1109/TIT.2007.899484
Abstract
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of independent random variables to the information contained in sums over subsets of the random variables, for an arbitrary collection of subsets. As a consequence, a simple proof of the monotonicity of information in central limit theorems is obtained, both in the setting of i.i.d. summands as well as in the more general setting of independent summands with variance-standardized sums.
13 pages. Many minor modifications from first version, plus a section on refined results. This is almost but not exactly identical to the published version
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