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Statistical Inference for Rényi Entropy Functionals

  • David Källberg
  • Nikolaj Leonenko
  • Oleg Seleznjev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7260)

Abstract

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

Keywords

entropy estimation Rényi entropy U-statistics approximate matching asymptotic normality 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • David Källberg
    • 1
  • Nikolaj Leonenko
    • 2
  • Oleg Seleznjev
    • 1
  1. 1.Department of Mathematics and Mathematical StatisticsUmeå UniversityUmeåSweden
  2. 2.School of MathematicsCardiff UniversityCardiffUK

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