Further investigations of R\'enyi entropy power inequalities and an entropic characterization of s-concave densities
| Autor: | Li, Jiange, Marsiglietti, Arnaud, Melbourne, James |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We investigate the role of convexity in R\'enyi entropy power inequalities. After proving that a general R\'enyi entropy power inequality in the style of Bobkov-Chistyakov (2015) fails when the R\'enyi parameter $r\in(0,1)$, we show that random vectors with $s$-concave densities do satisfy such a R\'enyi entropy power inequality. Along the way, we establish the convergence in the Central Limit Theorem for R\'enyi entropies of order $r\in(0,1)$ for log-concave densities and for compactly supported, spherically symmetric and unimodal densities, complementing a celebrated result of Barron (1986). Additionally, we give an entropic characterization of the class of $s$-concave densities, which extends a classical result of Cover and Zhang (1994). Comment: 20 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|