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Entropy and Random Vectors

Entropy and Random Vectors Barron(1) produced a proof of the Central Limit Theorem for real-valued IID random variables, in the sense of convergence in relative entropy. Here, we establish a similar result for independent real-valued random vectors, not necessarily identically distributed. The main developments required are a generalisation of De Bruijn's identity, and various inequalities proposed in ref. 2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

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References (12)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Plenum Publishing Corporation
Subject
Physics; Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
DOI
10.1023/A:1010353526846
Publisher site
See Article on Publisher Site

Abstract

Barron(1) produced a proof of the Central Limit Theorem for real-valued IID random variables, in the sense of convergence in relative entropy. Here, we establish a similar result for independent real-valued random vectors, not necessarily identically distributed. The main developments required are a generalisation of De Bruijn's identity, and various inequalities proposed in ref. 2.

Journal

Journal of Statistical PhysicsSpringer Journals

Published: Oct 7, 2004

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