Kybernetika 53 no. 2, 231-243, 2017

A subcopula based dependence measure

Arturo ErdelyDOI: 10.14736/kyb-2017-2-0231

Abstract:

A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided, along with an R package to perform the corresponding calculations.

Keywords:

concordance, dependence, subcopula

Classification:

62H20

paper.pdf

References:

  1. D. M. Cifarelli, P. L. Conti and E. Regazzini: On the asymptotic distribution of a general measure of monotone dependence. Ann. Statist. 24 (1996), 1386-1399.   DOI:10.1214/aos/1032526975
  2. M. Denuit and P. Lambert: Constraints on concordance measures in bivariate discrete data. J. Mult. Anal. 93 (2005), 40-57.   DOI:10.1016/j.jmva.2004.01.004
  3. F. Durante and C. Sempi: Principles of Copula Theory. CRC Press, Boca Raton 2016.   DOI:10.1201/b18674
  4. A. Erdely: subcopem2D: Bivariate Empirical Copula. R package version 1.2 (2017), URL   https://CRAN.R-project.org/package=subcopem2D
  5. C. Genest and J. Nešlehová: A primer on copulas for count data. Astin Bull. 37 (2007), 475-515.   DOI:10.2143/ast.37.2.2024077
  6. C. Genest, J. Nešlehová and B. Rémillard: On the empirical multilinear copula process for count data. Bernoulli 20 (2014), 1344-1371.   DOI:10.3150/13-bej524
  7. M. Hofert, I. Kojadinovic, M. Maechler and J. Yan: copula: Multivariate Dependence with Copulas. R package version 0.999-16 (2017), URL   https://CRAN.R-project.org/package=copula
  8. E. L. Lehmann: Some concepts of dependence. Ann. Math. Statist. 37 (1966), 1137-1153.   DOI:10.1214/aoms/1177699260
  9. X. Li, P. Mikusiński, H. Sherwood and M. D Taylor: On approximation of copulas. In: Distributions with given marginals and moment problems (V. Beneš and J. Štěpán, eds.), Kluwer, Dordrecht 1997, pp. 107-116.   DOI:10.1007/978-94-011-5532-8_13
  10. R. B. Nelsen: An Introduction to Copulas. Springer, New York 2006.   DOI:10.1007/0-387-28678-0
  11. J. Nešlehová: On rank correlation measures for non-continuous random variables. J. Mult. Anal. 98 (2007), 544-567.   DOI:10.1016/j.jmva.2005.11.007
  12. R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing (Vienna), URL   https://www.R-project.org/
  13. M. Scarsini: On measures of concordance. Stochastica 8 (1984), 201-218.   CrossRef
  14. B. Schweizer and E. F. Wolff: On nonparametric measures of dependence for random variables. Ann. Statist. 9 (1981), 879-885.   DOI:10.1214/aos/1176345528
  15. A. Sklar: Fonctions de répartition à $n$ dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231.   CrossRef