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Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma

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  • Eguchi, Shinto
  • Copas, John

Abstract

Kullback-Leibler divergence and the Neyman-Pearson lemma are two fundamental concepts in statistics. Both are about likelihood ratios: Kullback-Leibler divergence is the expected log-likelihood ratio, and the Neyman-Pearson lemma is about error rates of likelihood ratio tests. Exploring this connection gives another statistical interpretation of the Kullback-Leibler divergence in terms of the loss of power of the likelihood ratio test when the wrong distribution is used for one of the hypotheses. In this interpretation, the standard non-negativity property of the Kullback-Leibler divergence is essentially a restatement of the optimal property of likelihood ratios established by the Neyman-Pearson lemma. The asymmetry of Kullback-Leibler divergence is overviewed in information geometry.

Suggested Citation

  • Eguchi, Shinto & Copas, John, 2006. "Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2034-2040, October.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:2034-2040
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    References listed on IDEAS

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    1. Shinto Eguchi, 2002. "A class of logistic-type discriminant functions," Biometrika, Biometrika Trust, vol. 89(1), pages 1-22, March.
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    Cited by:

    1. Gallindo, Lucas, 2007. "Computation of Power Loss in Likelihood Ratio Tests for Probability Densities Extended by Lehmann Alternatives," OSF Preprints pkcnb, Center for Open Science.
    2. Ghosh, Indranil, 2023. "On the issue of convergence of certain divergence measures related to finding most nearly compatible probability distribution under the discrete set-up," Statistics & Probability Letters, Elsevier, vol. 203(C).
    3. Springborn, Michael & Sanchirico, James N., 2013. "A density projection approach for non-trivial information dynamics: Adaptive management of stochastic natural resources," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 609-624.
    4. Piyush Anand & Clarence Lee, 2023. "Using Deep Learning to Overcome Privacy and Scalability Issues in Customer Data Transfer," Marketing Science, INFORMS, vol. 42(1), pages 189-207, January.
    5. Valdevino Félix de Lima, Wenia & David Costa do Nascimento, Abraão & José Amorim do Amaral, Getúlio, 2021. "Distance-based tests for planar shape," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    6. Jinxin Liu & Guan Wang & Tong Zhao & Li Zhang, 2017. "Fault Diagnosis of On-Load Tap-Changer Based on Variational Mode Decomposition and Relevance Vector Machine," Energies, MDPI, vol. 10(7), pages 1-14, July.
    7. Bhattacharya, Bhaskar & Hughes, Gareth, 2015. "On shape properties of the receiver operating characteristic curve," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 73-79.

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