Statistical inference for the ϵ-entropy and the quadratic Rényi entropy

Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Seleznjev, Oleg 2010. Statistical inference for the ϵ-entropy and the quadratic Rényi entropy. Journal of Multivariate Analysis 101 (9) , pp. 1981-1994. 10.1016/j.jmva.2010.05.009

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Abstract

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 ϵ-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 identification problems, average case analysis for random databases, approximate pattern matching in bioinformatics, cryptography).

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Entropy estimation; Quadratic Rényi entropy; U-statistics
Publisher:	Elsevier
ISSN:	0047-259X
Last Modified:	18 Oct 2022 13:27
URI:	https://orca.cardiff.ac.uk/id/eprint/13897

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