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Tytuł artykułu

Copula-based dependence measures

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of the present paper is to examine two wide classes of dependence coefficients including several well-known coefficients, for example Spearman’s ρ, Spearman’s footrule, and the Gini coefficient. There is a close relationship between the two classes: The second class is obtained by a symmetrisation of the coefficients in the former class. The coefficients of the first class describe the deviation from monotonically increasing dependence. The construction of the coefficients can be explained by geometric arguments. We introduce estimators of the dependence coefficients and prove their asymptotic normality.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-05-23
zaakceptowano
2014-09-17
online
2014-10-10
Twórcy
  • University of Applied Sciences Merseburg, Department of Computer Science
    and Communication Systems, D-06217 Merseburg, Germany
Bibliografia
  • [1] Behboodian, J; Dolati, A.; Úbeda-Flores, M. (2007). A multivariate version of Gini’s rank association coeflcient. Statist.Papers 48, 295-304.
  • [2] Cifarelli, D.M.; Conti, P.L.; Regazzini, E. (1996). On the asymptotic distribution of a general measure of monotone dependence.Ann. Statist. 24, 1386-1399.
  • [3] Dolati, A.; Úbeda-Flores, M. (2006). On measures of multivariate concordance. J. Probab. Statist. Sci. 4, 147-163.
  • [4] Gaißer, S.; Ruppert, M.; Schmid, F. (2010). A multivariate version of Hoeffding’s Phi-Square. J. Multivariate Anal. 101, 2571-2586.
  • [5] Genest, C.; Nešlehová, J.; Rémillard (2013). On the estimation of Spearman’s rho and related tests of independence forpossibly discontinuous multivariate data. J. Multivariate Anal. 117, 214-228.
  • [6] Grothe, O.; Schmid, F.; Schnieders, J.; Segers, J. (2014). Measuring Association between Random Vectors. J. MultivariateAnal. 123, 96-110.
  • [7] Joe, H. (1990). Multivariate concordance. J. Multivariate Anal. 35, 12-30.
  • [8] Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall.
  • [9] Nelsen, R.B. (2006). An Introduction to Copulas, Springer, Second Edition.
  • [10] Scarsini, M. (1984). On measures of concordance. Stochastica 8, 201-218.
  • [11] Schmid, F., Schmidt, R. (2007a). Multivariate extensions of Spearman’s rho and related statistics. Statist. Probab. Lett. 77,407-416.
  • [12] Schmid, F., Schmidt, R. (2007b). Nonparametric inference onmultivariate versions of Blomqvist’s beta and relatedmeasuresof tail dependence. Metrika 66, 323-354.
  • [13] Schmid, F.; Schmidt, R.; Blumentritt, T.; Gaißer, S.; Ruppert, M. (2010). Copula-based measures of multivariate association.in F. Durante, W. Härdle, P. Jaworski, T. Rychlik (eds.) Copula Theory and Its Applications. Springer Berlin, 2010.
  • [14] Schweizer, B.; Wolff, E.F. (1981). On nonparametric measures of dependence for random variables. Ann. Statist. 9, 879-885.
  • [15] Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
  • [16] Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique deL’Université de Paris 8, 229-231.
  • [17] Taylor, M. D. (2007). Multivariate measures of concordance. Ann. Inst. Statist. Math. 59, 789-806.
  • [18] Úbeda-Flores, M. (2005). Multivariate versions of Blomqvist’s beta and Spearman’s footrule. Ann. lnst. Statist. Math. 57,781-788.
  • [19] Van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge University Press.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_demo-2014-0004
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