A multivariate version of Gini's rank association coefficient

Behboodian, Javad; Dolati, Ali; Úbeda-Flores, Manuel

doi:10.1007/s00362-006-0332-9

Cited by 31 publications

(25 citation statements)

References 3 publications

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“…−1  Moreover, as Behboodian et al [19] point out, the function  0  can be extended to the case in which either  or  0 is a measurable function from I  to I, as it will happen when  =  , for instance.…”

Section: Concordancementioning

confidence: 99%

“…In the trivariate case, Behboodian et al [19] show that the trivariate Gini's gamma for ( 1   2   3 ) is just the average of the three corresponding pairwise Gini's coefficients, that is…”

Section: A Multivariate Version Of Gini's Gammamentioning

confidence: 99%

“…Furthermore, Behboodian et al [19] provides the sample version of the coefficient   and show that, in the trivariate case, the relationship (13) also holds for the corresponding sample versions, that is…”

Section: A Multivariate Version Of Gini's Gammamentioning

confidence: 99%

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Measuring the Dependence Among Dimensions of Welfare: A Study Based on Spearman’s Footrule and Gini’s Gamma

Pérez

Alaiz

2016

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Welfare is multidimensional as it involves not only income, but also education, health or labour. The composite indicators of welfare are usually based on aggregating somehow the information across dimensions and individuals. However, this approach ignores the relationship between the dimensions being aggregated. To face this goal, in this paper we analyse the dependence between the dimensions included in the Human Development Index (HDI), namely income, health and schooling, through three copula-based measures of multivariate association: Spearman's footrule, Gini's gamma and Spearman's rho. We discuss their properties and prove new results on Spearman's footrule. The copula approach focuses on the positions of the individuals across dimensions, rather than the values that the variables attain for such individuals. Thus, it allows for more general types of dependence than the linear correlation. We base our study on data from 1980 till 2014 for the countries included in the 2015 Human Development Report. We find out that though the overall HDI has increased over this period, the dependence between its dimensions remains high and nearly unchanged so that the richest countries tend to be also the best ranked in both health and education.

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Section: Concordancementioning

confidence: 99%

Section: A Multivariate Version Of Gini's Gammamentioning

confidence: 99%

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Measuring the Dependence Among Dimensions of Welfare: A Study Based on Spearman’s Footrule and Gini’s Gamma

Pérez

Alaiz

2016

Int. J. Unc. Fuzz. Knowl. Based Syst.

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“…(See [13] and [15] for an overview.) Some instances of a desire to push the use of copulas into higher dimensions are [2], [6], [12], and [16] where copulas are used to investigate measures of concordance.…”

Section: Markov Operators On L ∞ (I)mentioning

confidence: 99%

Markov operators and n-copulas

Mikusiński

Taylor

2009

Ann. Polon. Math.

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“…This new measure differs from other multivariate dependence measures in e.g. Wolff (1980), Fernández Fernández andGonzález-Barrios (2004), Taylor (2007), Behboodian et al (2007), Schmid and Schmidt (2007) or Koch and De Schepper (2011), as it focuses on the aggregate risk S rather than on the copula or the joint distribution function of X . In a finance context, it can be translated into a measure for herd behavior, see Dhaene et al (2012).…”

Section: Introductionmentioning

confidence: 97%

A multivariate dependence measure for aggregating risks

Dhaene

Linders

Schoutens

et al. 2014

Journal of Computational and Applied Mathematics

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To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other hand, assuming a comonotonic dependence structure will likely overrate the real aggregate risk. In order to choose between both approximations, or perhaps use a weighted average, we should have an indication on the accuracy. Clearly this accuracy will depend on the copula between the individual risk factors, but it is also influenced by the marginal distributions. In this paper we introduce a multivariate dependence measure that takes both aspects into account. This new measure differs from other multivariate dependence measures, as it focuses on the aggregate risk rather than on the copula or the joint distribution function itself. We prove several interesting properties of this new measure and discuss its relation to other dependence measures. We also give some comments on the estimation and conclude with examples and numerical results.

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A multivariate version of Gini's rank association coefficient

Abstract: Primary 62H05, Secondary 62H20, Copulas, Gini's coefficient, Multivariate association,

Cited by 31 publications

References 3 publications

Measuring the Dependence Among Dimensions of Welfare: A Study Based on Spearman’s Footrule and Gini’s Gamma

Measuring the Dependence Among Dimensions of Welfare: A Study Based on Spearman’s Footrule and Gini’s Gamma

Markov operators and n-copulas

A multivariate dependence measure for aggregating risks

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