The aim of this contribution consists in defining concordance measures in a multivariate context, recurring to statistical tools such as the Lorenz concentration curve and the dual Lorenz curve. In particular, the definition of a k-variate (k > 2) concordance index recurring to the ranks-based approach, can be stated by exploiting the connection between the second stochastic dominance and the generalized Lorenz curve according to which establishing an ordering to define the concordance degree among all the involved variables. Another result consists in the proof of the relationship between the dual Lorenz curve and the ROC curve for which a Lorenz dominance result can be established.
On dependence measures in a multivariate context
GIUDICI, PAOLO STEFANO;RAFFINETTI, EMANUELA
2009-01-01
Abstract
The aim of this contribution consists in defining concordance measures in a multivariate context, recurring to statistical tools such as the Lorenz concentration curve and the dual Lorenz curve. In particular, the definition of a k-variate (k > 2) concordance index recurring to the ranks-based approach, can be stated by exploiting the connection between the second stochastic dominance and the generalized Lorenz curve according to which establishing an ordering to define the concordance degree among all the involved variables. Another result consists in the proof of the relationship between the dual Lorenz curve and the ROC curve for which a Lorenz dominance result can be established.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
