publication . Article . 2010

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

Leonenko, Nikolaj; Seleznjev, Oleg;
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  • Published: 01 Oct 2010 Journal: Journal of Multivariate Analysis, volume 101, pages 1,981-1,994 (issn: 0047-259X, Copyright policy)
  • Publisher: Elsevier BV
Abstract
AbstractEntropy 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 statist...
Subjects
free text keywords: Statistics, Probability and Uncertainty, Statistics and Probability, Numerical Analysis, Rényi entropy, Asymptotic distribution, Independent and identically distributed random variables, Mathematics, Econometrics, Mathematical statistics, Statistics, Maximum entropy probability distribution, Probability distribution, Asymptotic theory (statistics), Principle of maximum entropy, Entropy estimation, Quadratic Rényi entropy, U-statistics
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