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Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades

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  • Asok K. Nanda
  • Shovan Chowdhury

Abstract

Starting from the pioneering works of Shannon and Weiner in 1948, a plethora of works have been reported on entropy in different directions. Entropy‐related review work in the direction of statistical inference, to the best of our knowledge, has not been reported so far. Here, we have tried to collect all possible works in this direction during the last seven decades so that people interested in entropy, specially the new researchers, get benefited.

Suggested Citation

  • Asok K. Nanda & Shovan Chowdhury, 2021. "Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades," International Statistical Review, International Statistical Institute, vol. 89(1), pages 167-185, April.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:1:p:167-185
    DOI: 10.1111/insr.12374
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    References listed on IDEAS

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    1. Burbea, Jacob & Rao, C. Radhakrishna, 1982. "Entropy differential metric, distance and divergence measures in probability spaces: A unified approach," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 575-596, December.
    2. Sangun Park & Johan Lim, 2015. "On censored cumulative residual Kullback–Leibler information and goodness-of-fit test with type II censored data," Statistical Papers, Springer, vol. 56(1), pages 247-256, February.
    3. Alwan, Layth C. & Ebrahimi, Nader & Soofi, Ehsan S., 1998. "Information theoretic framework for process control," European Journal of Operational Research, Elsevier, vol. 111(3), pages 526-542, December.
    4. V. Zardasht & S. Parsi & M. Mousazadeh, 2015. "On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality," Statistical Papers, Springer, vol. 56(3), pages 677-688, August.
    5. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    6. Brockett, Patrick L. & Charnes, Abraham & Cooper, William W. & Learner, David & Phillips, Fred Y., 1995. "Information theory as a unifying statistical approach for use in marketing research," European Journal of Operational Research, Elsevier, vol. 84(2), pages 310-329, July.
    7. Jonggun Lim & Sangun Park, 2007. "Censored Kullback-Leibler Information and Goodness-of-Fit Test with Type II Censored Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(9), pages 1051-1064.
    8. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    9. Valérie Girardin & Philippe Regnault, 2016. "Escort distributions minimizing the Kullback–Leibler divergence for a large deviations principle and tests of entropy level," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 439-468, April.
    10. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 683-697, December.
    11. Park, Sangun, 1999. "A goodness-of-fit test for normality based on the sample entropy of order statistics," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 359-363, October.
    12. Peter Hall & Sally Morton, 1993. "On the estimation of entropy," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(1), pages 69-88, March.
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    1. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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