Generalized Entropy Power Inequalities and Monotonicity Properties of Information
<|reference_start|>Generalized Entropy Power Inequalities and Monotonicity Properties of Information: 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 $n$ 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.<|reference_end|>
@article{madiman2006generalized,
    title={Generalized Entropy Power Inequalities and Monotonicity Properties of
  Information},
    author={Mokshay Madiman and Andrew Barron},
    journal={IEEE Transactions on Information Theory, Vol. 53(7), pp.
  2317-2329, July 2007},
    year={2006},
    doi={10.1109/TIT.2007.899484},
    archivePrefix={arXiv},
    eprint={cs/0605047},
    primaryClass={cs.IT math.IT math.PR math.ST stat.TH}
}