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Statistical inference for the epsilon-entropy and the quadratic Renyi entropy
School of Mathematics, Cardi® University, Senghennydd Road, Cardi® CF24 4AG, UK.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 101, no 9, 1981-1994 p.Article in journal (Refereed) Published
Abstract [en]

Entropy and its various generalizations are widely used in mathematical statistics, communication theory, physical and computer sciences for characterizing the amount of information in a probability distribution. We consider estimators of the quadratic Rényi entropy and some related characteristics of discrete and continuous probability distributions based on the number of coincident (or-close) vector observations in the corresponding independent and identically distributed sample. We show some asymptotic properties of these estimators (e.g., consistency and asymptotic normality). These estimators can be used in various problems in mathematical statistics and computer science (e.g., distribution identi¯cation problems, average case analysis for random databases, approximate pattern matching in bioinformatics, cryptography).

Place, publisher, year, edition, pages
2010. Vol. 101, no 9, 1981-1994 p.
Keyword [en]
Entropy estimation, Quadratic Rényi entropy, U-statistics
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-60747DOI: 10.1016/j.jmva.2010.05.009ISI: 000280566400007OAI: diva2:562502
Available from: 2012-11-15 Created: 2012-10-24 Last updated: 2012-11-15Bibliographically approved

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Seleznjev, Oleg
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