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Measures of Mutually Complete Dependence for Discrete Random Vectors

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Predictive Econometrics and Big Data (TES 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 753))

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Abstract

In this paper, a marginal-free measure of mutually complete dependence for discrete random vectors through subcopulas is defined, which generalizes the corresponding results for discrete random variables. Properties of the measure are studied and an estimator of the measure is introduced. Several examples are given for illustration of our results.

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References

  1. Agresti, A., Kateri, M.: Categorical Data Analysis, 2nd edn. Springer, Hoboken (2011)

    MATH  Google Scholar 

  2. Boonmee, T., Tasena, S.: Measure of complete dependence of random vectors. J. Math. Anal. Appl. 443(1), 585–595 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dette, H., Siburg, K.F., Stoimenov, P.A.: A copula-based non-parametric measure of regression dependence. Scand. J. Stat. 40(1), 21–41 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Genest, C., Quesada Molina, J., Rodríguez Lallena, J.: De l’impossibilité de construire des lois à marges multidimensionnelles données à partir de copules. Comptes rendus de l’Académie des sciences. Série 1, Mathématique 320(6), 723–726 (1995)

    MATH  Google Scholar 

  5. Lancaster, H.: Measures and indices of dependence. In: Kotz, S., Johnson, N.L. (eds.) Encyclopedia of Statistical Sciences, vol. 2, pp. 334–339. Wiley, New York (1982)

    Google Scholar 

  6. Li, H., Scarsini, M., Shaked, M.: Linkages: a tool for the construction of multivariate distributions with given nonoverlapping multivariate marginals. J. Multivar. Anal. 56(1), 20–41 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)

    MATH  Google Scholar 

  8. Rényi, A.: On measures of dependence. Acta Math. Hung. 10(3–4), 441–451 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  9. Schweizer, B., Wolff, E.F.: On nonparametric measures of dependence for random variables. Ann. Stat. 9(4), 879–885 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shan, Q.: The measures of association and dependence through copulas. Ph.D. dissertation, New Mexico State University (2015)

    Google Scholar 

  11. Shan, Q., Wongyang, T., Wang, T., Tasena, S.: A measure of mutual complete dependence in discrete variables through subcopula. Int. J. Apporx. Reason. 65, 11–23 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Siburg, K.F., Stoimenov, P.A.: A measure of mutual complete dependence. Metrika 71(2), 239–251 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sklar, A.: Fonctions de répartition á \(n\) dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris 8, 229–231 (1959)

    MATH  Google Scholar 

  14. Tasena, S., Dhompongsa, S.: A measure of multivariate mutual complete dependence. Int. J. Apporx. Reason. 54(6), 748–761 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Tasena, S., Dhompongsa, S.: Measures of the functional dependence of random vectors. Int. J. Apporx. Reason. 68, 15–26 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Trutschnig, W.: On a strong metric on the space of copulas and its induced dependence measure. J. Math. Anal. Appl. 384(2), 690–705 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

We would like to thank Professor Hung T. Nguyen for introducing this interesting topic to us and referees for their valuable comments and suggestions which greatly improve this paper.

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Correspondence to Tonghui Wang .

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Zhu, X., Wang, T., Choy, S.T.B., Autchariyapanitkul, K. (2018). Measures of Mutually Complete Dependence for Discrete Random Vectors. In: Kreinovich, V., Sriboonchitta, S., Chakpitak, N. (eds) Predictive Econometrics and Big Data. TES 2018. Studies in Computational Intelligence, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-70942-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-70942-0_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70941-3

  • Online ISBN: 978-3-319-70942-0

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