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Directional dependence in multivariate distributions

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Abstract

In this paper, we develop some coefficients which can be used to detect dependence in multivariate distributions not detected by several known measures of multivariate association. Several examples illustrate our results.

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References

  • Cuadras C.M., Augé J. (1981) A continuous general multivariate distribution and its properties. Communications in Statistics A—Theory and Methods 10: 339–353

    Article  MathSciNet  Google Scholar 

  • Dolati A., Úbeda-Flores M. (2006) On measures of multivariate concordance. Journal of Probability and Statistical Sciences 4: 147–163

    Google Scholar 

  • Fisher, N. I. (1997). Copulas. In S. Kotz, C. B. Read, D. L. Banks (Eds.), Encyclopedia of statistical sciences (Vol. 1, pp. 159–163). New York: Wiley.

  • Joe H. (1990) Multivariate concordance. Journal of Multivariate Analysis 35: 12–30

    Article  MathSciNet  MATH  Google Scholar 

  • Joe H. (1997) Multivariate models and dependence concepts. Chapman & Hall, London

    MATH  Google Scholar 

  • Jogdeo, K. (1982). Concepts of dependence. In S. Kotz, N. L. Johnson (Eds.), Encyclopedia of statistical sciences (Vol. 1, pp. 324–334). New York: Wiley.

  • Johnson N.L., Kotz S. (1972) Distributions in statistics: continuous multivariate distributions. Wiley, New York

    MATH  Google Scholar 

  • Kimeldorf G., Sampson A.R. (1987) Positive dependence orders. Annals of the Institute of Statistical Mathematics 39: 113–128

    Article  MathSciNet  MATH  Google Scholar 

  • Kimeldorf G., Sampson A.R. (1989) A framework for positive dependence. Annals of the Institute of Statistical Mathematics 41: 31–45

    MathSciNet  MATH  Google Scholar 

  • McNeil A., Nešlehová J. (2009) Multivariate Archimedean copulas, d-monotone functions and l 1-norm symmetric distributions. Annals of Statistics 37: 3059–3097

    Article  MathSciNet  MATH  Google Scholar 

  • Mikusiński P., Sherwood H., Taylor M.D. (1992) Shuffles of Min. Stochastica 13: 61–74

    MathSciNet  MATH  Google Scholar 

  • Nelsen, R.B. (1996). Nonparametric measures of multivariate association. In L. Rüschendorf, B. Schweizer, M. D. Taylor (Eds.), Distributions with given marginals and related topics. IMS Lecture Notes-Monograph Series (Vol. 28, pp. 223–232). Hayward, CA: Institute of Mathematical Statistics.

  • Nelsen R.B. (2006) An introduction to copulas (2nd edn). Springer, New York

    MATH  Google Scholar 

  • Quesada-Molina, J. J., Rodríguez-Lallena, J. A., Úbeda-Flores, M. (2011). Directional dependence (to appear).

  • Schmid F., Schmidt R. (2007) Multivariate extensions of Spearman’s rho and related statistics. Statistics and Probability Letters 77: 407–416

    Article  MathSciNet  MATH  Google Scholar 

  • Sklar A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris 8: 229–231

    MathSciNet  Google Scholar 

  • Taylor M.D. (2007) Multivariate measures of concordance. Annals of the Institute of Statistical Mathematics 59: 789–806

    Article  MathSciNet  MATH  Google Scholar 

  • Taylor, M. D. (2008). Some properties of multivariate measures of concordance. arXiv:0808.3105 [math.PR].

  • Úbeda-Flores M. (2005) Multivariate versions of Blomqvist’s beta and Spearman’s footrule. Annals of the Institute of Statistical Mathematics 57: 781–788

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Lewis and Clark College, 0615 SW Palatine Hill Rd., Portland, OR, 97219, USA

    Roger B. Nelsen

  2. Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Carretera de Sacramento s/n, 04120, La Cañada de San Urbano, Almería, Spain

    Manuel Úbeda-Flores

Authors
  1. Roger B. Nelsen
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  2. Manuel Úbeda-Flores
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Correspondence to Manuel Úbeda-Flores.

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Nelsen, R.B., Úbeda-Flores, M. Directional dependence in multivariate distributions. Ann Inst Stat Math 64, 677–685 (2012). https://doi.org/10.1007/s10463-011-0329-6

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  • DOI: https://doi.org/10.1007/s10463-011-0329-6

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