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Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma
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Eguchi, Shinto and Copas, John B. (2006) Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma. JOURNAL OF MULTIVARIATE ANALYSIS, 97 (9 Sp. Iss. SI). pp. 2034-2040. doi:10.1016/j.jmva.2006.03.007 ISSN 0047-259X.
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Official URL: http://dx.doi.org/10.1016/j.jmva.2006.03.007
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. (c) 2006 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | JOURNAL OF MULTIVARIATE ANALYSIS | ||||
Publisher: | ELSEVIER INC | ||||
ISSN: | 0047-259X | ||||
Official Date: | October 2006 | ||||
Dates: |
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Volume: | 97 | ||||
Number: | 9 Sp. Iss. SI | ||||
Number of Pages: | 7 | ||||
Page Range: | pp. 2034-2040 | ||||
DOI: | 10.1016/j.jmva.2006.03.007 | ||||
Publication Status: | Published |
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