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Generalized Mutual-Information Based Independence Tests

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Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

We derive independence tests by means of dependence measures thresholding in a semiparametric context. Precisely, estimates of mutual information associated to \(\varphi \)-divergences are derived through the dual representations of \(\varphi \)-divergences. The asymptotic properties of the estimates are established, including consistency, asymptotic distribution and large deviations principle. The related tests of independence are compared through their relative asymptotic Bahadur efficiency and numerical simulations.

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References

  1. Broniatowski, M., Keziou, A.: Minimization of \(\phi \)-divergences on sets of signed measures. Studia Sci. Math. Hung. 43(4), 403–442 (2006). arXiv:1003.5457

    MathSciNet  MATH  Google Scholar 

  2. Eichelsbacher, P., Schmock, U.: Large deviations of \(U\)-empirical measures in strong topologies and applications. Ann. Inst. Henri Poincaré Probab. Stat. 38(5), 779–797 (2002)

    MathSciNet  MATH  Google Scholar 

  3. Joe, H.: Multivariate Models and Dependence Concepts. Monographs on Statistics and Applied Probability, vol. 73. Chapman & Hall, London (1997). http://dx.doi.org/10.1201/b13150

    Book  MATH  Google Scholar 

  4. Keziou, A.: Dual representation of \(\phi \)-divergences and applications. C. R. Math. Acad. Sci. Paris 336(10), 857–862 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Keziou, A., Regnault, P.: Semiparametric estimation of mutual information and related criteria: Optimal test of independence. Manuscript in preparation (2015)

    Google Scholar 

  6. Khan, S., Bandyopadhyay, S., Ganguly, A.R., Saigal, S., Erickson, D.J., Protopopescu, V., Ostrouchov, G.: Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data. Phys. Rev. E 76, 026209 (2007). http://link.aps.org/doi/10.1103/PhysRevE.76.026209

    Article  MathSciNet  Google Scholar 

  7. Nelsen, R.B.: An Introduction to Copulas. Springer Series in Statistics, Second edn. Springer, New York (2006)

    MATH  Google Scholar 

  8. Pardo, L.: Statistical Inference Based on Divergence Measures. Statistics: Textbooks and Monographs, vol. 185. Chapman & Hall/CRC, Boca Raton (2006)

    MATH  Google Scholar 

  9. van der Vaart, A.W.: Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques de Reims, EA 4535, UFR Sciences Exactes et Naturelles, Moulin de la Housse, BP1039, 51687, Remis Cedex, France

    Amor Keziou & Philippe Regnault

Authors
  1. Amor Keziou
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  2. Philippe Regnault
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Corresponding author

Correspondence to Philippe Regnault .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Keziou, A., Regnault, P. (2015). Generalized Mutual-Information Based Independence Tests. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_49

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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