CONCENTRATION OF THE INFORMATION IN DATA WITH LOG-CONCAVE DISTRIBUTIONS

被引：55
作者：
Bobkov, Sergey [1 ]
Madiman, Mokshay [2 ]
机构：
[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
[2] Yale Univ, Dept Stat, New Haven, CT 06511 USA
来源：
ANNALS OF PROBABILITY | 2011年 / 39卷 / 04期
关键词：
Concentration; entropy; log-concave distributions; asymptotic equipartition property; Shannon-McMillan-Breiman theorem; MCMILLAN-BREIMAN THEOREM; ERGODIC THEOREM; SPACES; PROOF;
D O I：
10.1214/10-AOP592
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
A concentration property of the functional - log f (X) is demonstrated, when a random vector X has a log-concave density f on R-n. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.
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页码：1528 / 1543
页数：16
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