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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Statistical Inference for Rényi Entropy Functionals
verfasst von : David Källberg, Nikolaj Leonenko, Oleg Seleznjev
Erschienen in: Conceptual Modelling and Its Theoretical Foundations
Verlag: Springer Berlin Heidelberg
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Numerous entropy-type characteristics (functionals) generalizing Rényi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and distribution identification problems. We consider estimators of some entropy (integral) functionals for discrete and continuous distributions based on the number of epsilon-close vector records in the corresponding independent and identically distributed samples from two distributions. The proposed estimators are generalized
U
-statistics. We show the asymptotic properties of these estimators (e.g., consistency and asymptotic normality). The results can be applied in various problems in computer science and mathematical statistics (e.g., approximate matching for random databases, record linkage, image matching).
AMS 2000 subject classification:
94A15, 62G20