Moment-entropy inequalities for a random vector

Research output: Contribution to journalArticle

Abstract

The pth moment matrix is defined for a real random vector, generalizing the classical covariance matrix. Sharp inequalities relating the pth moment and Renyi entropy are established, generalizing the classical inequality relating the second moment and the Shannon entropy. The extremal distributions for these inequalities are completely characterized.

Original languageEnglish (US)
Pages (from-to)1603-1607
Number of pages5
JournalIEEE Transactions on Information Theory
Volume53
Issue number4
DOIs
StatePublished - Apr 2007

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entropy
Entropy
Covariance matrix

Keywords

  • Covariance
  • Covariance matrix
  • Entropy
  • Information measure
  • Information theory
  • Moment
  • Moment matrix
  • Random vector
  • Renyi entropy

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Information Systems

Cite this

Moment-entropy inequalities for a random vector. / Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: IEEE Transactions on Information Theory, Vol. 53, No. 4, 04.2007, p. 1603-1607.

Research output: Contribution to journalArticle

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