Multivariate Ranks-Based Concordance Indexes

  • Emanuela RaffinettiEmail author
  • Paolo Giudici
Conference paper
Part of the Studies in Theoretical and Applied Statistics book series (STAS)


The theoretical contributions to a “good” taxation have put the attention on the relations between the efficiency and the vertical equity without considering the “horizontal equity” notion: only recently, measures connected to equity (iniquity) of a taxation have been introduced in literature. The taxation problem is limited to the study of two quantitative characters: however the concordance problem can be extended in a more general context as we present in the following sections. In particular, the aim of this contribution consists in defining concordance indexes, as dependence measures, in a multivariate context. For this reason a k-variate (k > 2) concordance index is provided recurring to statistical tools such as ranks-based approach and multiple linear regression function. All the theoretical topics involved are shown through a practical example.


Linear Regression Model Gini Index Lorenz Curve Residual Deviance Concordance Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors acknowledge financial support from the European grant EU-IP MUSING (contract number 027097). The paper is the result of the close collaboration among the authors, however, it has been written by Emanuela Raffinetti with the supervision of Prof. Paolo Giudici.


  1. Leti, G.: Statistica descrittiva. Il Mulino (1983)Google Scholar
  2. Muliere, P.: Alcune osservazioni sull’equità orizzontale di una tassazione. Scritti in onore di Francesco Brambilla. Ed. by Bocconi Comunicazione 2, (Milano, 1986)Google Scholar
  3. Musgrave, R.A.: The Theory of Public Finance. New York, Mc Graw Hill (1959)Google Scholar
  4. Petrone, S., Muliere, P.: Generalized Lorenz curve and monotone dependence orderings. Metron Vol L, No. 3–4 (1992)Google Scholar
  5. Plotnick, R.: A Measure of Horizontal Inequity. The review of Economics and Statistics, 2, 283–288 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.University of PaviaPaviaItaly

Personalised recommendations