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The Gini Equivalents of the Covariance, the Correlation, and the Regression Coefficient

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The Gini Methodology

Part of the book series: Springer Series in Statistics ((SSS,volume 272))

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Abstract

Given two random variables, one may be interested in the correlation or association or concordance between them (Gili & Bettuzzi 1985). This purpose can be generalized by following Daniels who stated the target as “the degree of agreement” (Daniels, 1950, p. 171) between the order and the rank-order of two variables.

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Notes

  1. 1.

    1The complete proofs can be found in Schechtman and Yitzhaki (1987, 1999), Yitzhaki (2), and Serfling and Xiao (2007).

References

  • Barnett, V., Green, P. J., & Robinson, A. (1976). Concomitants and correlation estimates. Biometrika, 63, 323–328.

    Article  MATH  Google Scholar 

  • Barro, R. J. (1991). Economic growth in a cross-section of countries. Quarterly Journal of Economics, CVI, 407–444.

    Article  Google Scholar 

  • Barro, R. J., & Sala-i-Martin, X. (1992). Convergence. Journal of Political Economy, 100, 223–251.

    Article  Google Scholar 

  • Bliss, C. (1999). Galton’s fallacy and economic convergence. Oxford Economic Papers, 51, 4–14.

    Article  Google Scholar 

  • Blitz, R. C., & Brittain, J. A. (1964). An extension of the Lorenz diagram to the correlation of two variables. Metron, XXIII(1–4), 137–143.

    Google Scholar 

  • Boos, D. D. (1982). A test for asymmetry associated with the Hodges-Lehmann estimator. Journal of the American Statistical Association, 77(379 (September)), 647–651.

    Article  MathSciNet  MATH  Google Scholar 

  • Cambanis, S. (1991). On Eyraud–Farlie–Gumbel–Morgenstern random processes. In G. Dall’Aglio et al. (Eds.), Advances in probability distributions with given marginals. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Conover, W. J. (1980). Practical nonparametric statistics (2nd ed.). New York: John Wiley & Sons.

    Google Scholar 

  • Daniels, H. E. (1944). The relation between measures of correlation in the universe of sample permutation. Biometrika, 33, 129–135.

    Article  MathSciNet  MATH  Google Scholar 

  • Daniels, H. E. (1950). Rank correlation and population models. Journal of the Royal Statistical Society Series B (Methodological), 12(2), 171–191.

    MathSciNet  MATH  Google Scholar 

  • De Veaux, D. R. (1976). Tight upper and lower bounds for correlation of bivariate distributions arising in air pollution modeling. Technical Report No. 5 (1976), Department of Statistics, Stanford University.

    Google Scholar 

  • Denuit, M., & Dhaene, J. (2). Simple characterizations of comonotonicity and countermonotonicity by extremal correlations. Belgian Actuarial Bulletin, 3, 22–27.

    Google Scholar 

  • Durbin, J. (1954). Errors in Variables. Review of International Statistical Institute, 22, 23–32.

    Article  MathSciNet  Google Scholar 

  • Friedman, M. (1992). Do old fallacies ever die? Journal of Economic Literature, 30, 2129–2132.

    Google Scholar 

  • Galton, F. (1888). Co-relations and their measurement, chiefly from anthropometric data. Proceedings of the Royal Society of London, 45, 135–145.

    Article  Google Scholar 

  • Gili, A., & Bettuzzi, G. (1985). Concordance, ch. 6. In A. Naddeo (Ed.), Italian contributions to the methodology of statistics (pp. 231–243). Padova: Societá Italiana di Statistica.

    Google Scholar 

  • Gini, C. (1936). Sur le coefficient de correlation comme caracteristique du degree de la concordance. Review of the International Statistical Institute, 4(3), 355–366 (French).

    Article  Google Scholar 

  • Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. Annals of Mathematical statistics, 19, 293–325.

    Article  MathSciNet  MATH  Google Scholar 

  • Johnson, N. L., & Kotz, S. (1977). On some generalized Farlie-Gumbel-Morgenstern distributions–II: Regression, correlation, and further generalization. Communication in Statistics, 6, 485–496.

    Article  MathSciNet  Google Scholar 

  • Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30, 81–89.

    MathSciNet  MATH  Google Scholar 

  • Kendall, M. G. (1948). Rank correlation methods. London: Griffin& Co. (3rd ed., 1962).

    MATH  Google Scholar 

  • Kendall, M. G. (1955). Rank correlation methods (2nd ed.). New York: Hafner Publishing Company.

    MATH  Google Scholar 

  • Kotz, S., & Seeger, J. P. (1991). A new approach to dependence in multivariate distributions. In G. Dall’Aglio et al. (Eds.), Advances in probability distributions with given marginals. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Lambert, P. J., & Decoster, A. (2005). The Gini coefficient reveals more. Metron, LXIII(3), 373–400.

    MathSciNet  Google Scholar 

  • Lerman, R. I., & Yitzhaki, S. (1985). Income inequality effects by income source: A new approach and application to the U.S. Review of Economics and Statistics, 67, 151–156.

    Article  Google Scholar 

  • McCall, J. J. (1991). Exchangeability and its economic applications. Journal of Economic Dynamics and Control, 15, 549–568.

    Article  MathSciNet  Google Scholar 

  • Quah, D. T. (1993). Galton’s fallacy and tests of the convergence hypothesis. Scandinavian Journal of Economics, 95, 427–443.

    Article  Google Scholar 

  • Quah, D. T. (1996). Empirics for economic growth and convergence. European Economic Review, 40, 1353–1375.

    Article  Google Scholar 

  • Raveh, A. (1989). Gini correlation as a measure of monotonicity and two of its usages. Communication in Statistics, Theory and Methods, 18(4), 1415–1423.

    Article  MathSciNet  MATH  Google Scholar 

  • Sala-i-Martin, X. (1996). Regional cohesion: Evidence and theories of regional growth and convergence. European Economic Review, 40, 1325–1352.

    Article  Google Scholar 

  • Schechtman, E., & Yitzhaki, S. (1987). A measure of association based on Gini’s mean difference. Communications in Statistics, Theory and Methods, 16, 207–231.

    Article  MathSciNet  MATH  Google Scholar 

  • Schechtman, E., & Yitzhaki, S. (1999). On the proper bounds of the Gini correlation. Economics Letters, 63(2), 133–138.

    Article  MathSciNet  MATH  Google Scholar 

  • Schweizer, B., & Wolff, E. F. (1981). On nonparametric measures of dependence for random variables. The Annals of Statistics, 9(4), 879–885.

    Article  MathSciNet  MATH  Google Scholar 

  • Serfling, R., & Xiao, P. (2007). A contribution to multivariate L-moments: L-comoment matrices. Journal of Multivariate Analysis, 98(2007), 1765–1781.

    Article  MathSciNet  MATH  Google Scholar 

  • Shalit, H., & Yitzhaki, S. (1984). Mean-Gini, portfolio theory and the pricing of risky assets. Journal of Finance, 39(5 (December)), 1449–1468.

    Article  MathSciNet  Google Scholar 

  • Shih, W. J., & Huang, W. (1992). Evaluating correlation with proper bounds. Biometrics, 48, 1027–1213.

    Article  Google Scholar 

  • Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15, 72–101.

    Article  Google Scholar 

  • Stigler, S. M. (1989). Francis Galton’s account of the invention of correlation. Statistical Science, 4(2), 73–86.

    Article  MathSciNet  MATH  Google Scholar 

  • Stuart, A. (1954). The Correlation between variate-values and ranks in samples from a continuous distributions. British Journal of Statistical Psychology, 7, 37–44.

    Article  MathSciNet  Google Scholar 

  • Wodon, Q., & Yitzhaki, S. (2006). Convergence forward and backward. Economics Letters, 92, 47–51.

    Article  MathSciNet  MATH  Google Scholar 

  • Yitzhaki, S. (2). Gini’s mean difference: A superior measure of variability for non-normal distributions. Metron, LXI(2), 285–316.

    MathSciNet  Google Scholar 

  • Yitzhaki, S., & Olkin, I. (1991). Concentration indices and concentration curves. In Karl Mosler and Marco Scarsini (Eds.), Stochastic orders and decisions under risk, 19 (pp. 380–392). Institute Of Mathematical Statistics: Lecture-Notes Monograph Series.

    Google Scholar 

  • Yitzhaki, S., & Schechtman, E. (2004). The Gini instrumental variable, or the “double instrumental variable” estimator. Metron, LXII(3), 287–313.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Economics, The Hebrew University, Mount Scopus, Jerusalem, Israel

    Shlomo Yitzhaki

  2. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Edna Schechtman

Authors
  1. Shlomo Yitzhaki
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  2. Edna Schechtman
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Yitzhaki, S., Schechtman, E. (2013). The Gini Equivalents of the Covariance, the Correlation, and the Regression Coefficient. In: The Gini Methodology. Springer Series in Statistics, vol 272. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4720-7_3

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