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Statistical estimation of quadratic Rényi entropy for a stationary m -dependent sequence

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  • David Källberg
  • Nikolaj Leonenko
  • Oleg Seleznjev

Abstract

The Rényi entropy is a generalisation of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m -dependent sequence. The U -statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g. consistency, asymptotic normality, and Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g. ε-keys in time series databases and distribution identification problems for dependent samples).

Suggested Citation

  • David Källberg & Nikolaj Leonenko & Oleg Seleznjev, 2014. "Statistical estimation of quadratic Rényi entropy for a stationary m -dependent sequence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 385-411, June.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:385-411
    DOI: 10.1080/10485252.2013.854438
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    References listed on IDEAS

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    1. Wang, Qiying, 1999. "On Berry-Esséen rates for m-dependent U-statistics," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 123-130, January.
    2. Tae Kim & Zhi-Ming Luo & Chiho Kim, 2011. "The central limit theorem for degenerate variable -statistics under dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 683-699.
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    Cited by:

    1. Vitor Hugo Ferreira & André da Costa Pinho & Dickson Silva de Souza & Bárbara Siqueira Rodrigues, 2021. "A New Clustering Approach for Automatic Oscillographic Records Segmentation," Energies, MDPI, vol. 14(20), pages 1-18, October.

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