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Sup-Sums Principles for F-Divergence and a New Definition for t-Entropy

Author

Listed:
  • V. I. Bakhtin

    (John Paul II Catholic University of Lublin
    Belarusian State University)

  • A. V. Lebedev

    (Belarusian State University
    University of Bialystok)

Abstract

The article presents new $${\sup }$$ sup -sums principles for integral F-divergence for arbitrary convex functions F on the whole real axis and arbitrary (not necessarily positive and normalized) measures. Among applications of these results, we work out a new ‘integral’ definition for t-entropy explicitly establishing its relation to Kullback–Leibler divergence.

Suggested Citation

  • V. I. Bakhtin & A. V. Lebedev, 2022. "Sup-Sums Principles for F-Divergence and a New Definition for t-Entropy," Journal of Theoretical Probability, Springer, vol. 35(1), pages 350-369, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01046-5
    DOI: 10.1007/s10959-020-01046-5
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    References listed on IDEAS

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    1. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
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