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Conference Paper: Limit theorems for the sample entropy of hidden Markov chains

TitleLimit theorems for the sample entropy of hidden Markov chains
Authors
KeywordsCentral limit theorem
Convergence behaviors
Entropy rates
Ergodics
Hidden Markov chains
Issue Date2011
PublisherIEEE.
Citation
The 2011 IEEE International Symposium on Information Theory (ISIT), St. Petersburg, Russia, 31 July-5 August 2011. In Proceedings of ISIT, 2011, p. 3009-3013 How to Cite?
AbstractThe Shannon-McMillan-Breiman theorem asserts that the sample entropy of a stationary and ergodic stochastic process converges to the entropy rate of the same process (as the sample size tends to infinity) almost surely. In this paper, we restrict our attention to the convergence behavior of the sample entropy of hidden Markov chains. Under certain positivity assumptions, we prove that a central limit theorem (CLT) with some Berry-Esseen bound for the sample entropy of a hidden Markov chain, and we use this CLT to establish a law of iterated logarithm (LIL) for the sample entropy. © 2011 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/135893
ISSN
References

 

DC FieldValueLanguage
dc.contributor.authorHan, Gen_HK
dc.date.accessioned2011-07-27T01:59:10Z-
dc.date.available2011-07-27T01:59:10Z-
dc.date.issued2011en_HK
dc.identifier.citationThe 2011 IEEE International Symposium on Information Theory (ISIT), St. Petersburg, Russia, 31 July-5 August 2011. In Proceedings of ISIT, 2011, p. 3009-3013en_HK
dc.identifier.issn0271-4655-
dc.identifier.urihttp://hdl.handle.net/10722/135893-
dc.description.abstractThe Shannon-McMillan-Breiman theorem asserts that the sample entropy of a stationary and ergodic stochastic process converges to the entropy rate of the same process (as the sample size tends to infinity) almost surely. In this paper, we restrict our attention to the convergence behavior of the sample entropy of hidden Markov chains. Under certain positivity assumptions, we prove that a central limit theorem (CLT) with some Berry-Esseen bound for the sample entropy of a hidden Markov chain, and we use this CLT to establish a law of iterated logarithm (LIL) for the sample entropy. © 2011 IEEE.en_HK
dc.languageengen_US
dc.publisherIEEE.-
dc.relation.ispartofProceedings of IEEE International Symposium on Information Theory, ISIT 2011en_HK
dc.rightsProceedings of IEEE International Symposium on Information Theory. Copyright © IEEE.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rights©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.-
dc.subjectCentral limit theorem-
dc.subjectConvergence behaviors-
dc.subjectEntropy rates-
dc.subjectErgodics-
dc.subjectHidden Markov chains-
dc.titleLimit theorems for the sample entropy of hidden Markov chainsen_HK
dc.typeConference_Paperen_HK
dc.identifier.emailHan, G:ghan@hku.hken_HK
dc.identifier.authorityHan, G=rp00702en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1109/ISIT.2011.6034131en_HK
dc.identifier.scopuseid_2-s2.0-80054802129en_HK
dc.identifier.hkuros187503en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80054802129&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.spage3009en_HK
dc.identifier.epage3013en_HK
dc.description.otherThe 2011 IEEE International Symposium on Information Theory (ISIT), St. Petersburg, Russia, 31 July-5 August 2011. In Proceedings of ISIT, 2011, p. 3009-3013-
dc.identifier.scopusauthoridHan, G=8640067800en_HK

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