Skip to main content
SpringerLink
Log in

Suggestions for Further Research

  • Chapter
  • First Online:
The Gini Methodology

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

  • 3277 Accesses

Abstract

Throughout the book we have stressed several properties that distinguish between the GMD and the variance, claiming that those properties give an advantage to using the GMD over the variance, in cases where the assumption of normality is not supported by the data. Among those properties are the following:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    This assumption is known as the “monotonicity assumption.” Additional assumptions that could be imposed on (23.1) below are local independence and local homogeneity (see Ellis & Wollenberg, 1993), but these additions are not relevant to our main argument.

  2. 2.

    These are assumptions of convenience; the conclusions reached here are not affected by allowing a “guessing parameter” to affect the item response function (see Lord, 1980, p. 12).

  3. 3.

    This section is based on Yitzhaki, Itzhaki and Pudalov, (2011).

  4. 4.

    See, for example, Wodon and Yitzhaki (2006) for a critique of the β convergence concept used in macro-economics in order to prove convergence in the growth rates of countries. Wodon and Yitzhaki found that this concept may lead both to convergence when moving forward and backward in time, which leads to a contradiction. See also O’Neill and Van Kerm (2008).

References

  • Barnett, V., & Lewis, T. (1978). Outliers in statistical data. Chinchester: John Wiley and Sons.

    MATH  Google Scholar 

  • Bassett, G., Jr., & Koenker, R. (1978). Asymptotic theory of least absolute error regression. Journal of the American Statistical Association, 73, 618–622.

    Article  MathSciNet  MATH  Google Scholar 

  • Bolt, D. M. (2). Conditional covariance-based presentation of multidimensional test structure. Applied Psychological Measurement, 25, 244–257.

    Article  MathSciNet  Google Scholar 

  • Calò, D. G. (2006). On a transvariation based measure of group separability. Journal of Classification, 23, 143–167.

    Article  MathSciNet  MATH  Google Scholar 

  • Chandra, M., & Singpurwalla, N. D. (1981). Relationships between some notions which are common to reliability theory and economics. Mathematics of Operations Research, 6(1 (February)), 113–121.

    Article  MathSciNet  MATH  Google Scholar 

  • Cheung, C. S., Clarence, C. K., & Peter, C. M. (2007). Mean-Gini portfolio analysis: A pedagogic illustration. Spreadsheets in Education (eJSiE), 2(2), 194–207.

    Google Scholar 

  • Cowell, F. A., & Fiorio, C. V. (2010). Inequality decompositions. A reconciliation. Mimeo.

    Google Scholar 

  • Ellis, J. L., & van den Wollenberg, A. L. (1993). Local homogeneity in latent trait models: A characterization of the homogeneous monotone IRT model. Psychometrika, 58(3 September), 417–429.

    Article  MathSciNet  MATH  Google Scholar 

  • Duclos, J.-Y., & Araar, A. (2006). Poverty and equity, measurement, policy, and estimation with DAD. Ottawa: Springer.

    Google Scholar 

  • Duclos, J.-Y., Araar, A., & Fortin, C. (2). DAD: A software for distributive analysis/analyse distributive. International Development Research Centre, Government of Canada, et CRÉFA, Laval University. http://www.mimap.ecn.ulaval.ca.

  • Gorard, S. (2005). Revisiting a 90-year-old debate: The advantages of the mean deviation. British Journal of Educational Studies, 53(4 (December)), 417–430.

    Article  Google Scholar 

  • Grunfeld, Y., & Griliches, Z. (1960). Is aggregation necessarily bad? Review of Economics and Statistics, 42(1 (February)), 1–13.

    Article  Google Scholar 

  • Huber, P. (1981). Robust statistics. New York: John Wiley and Sons.

    Book  MATH  Google Scholar 

  • Koenker, R. (2005). Quantile regression. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Koenker, R., & Bassett, G., Jr. (1978). Regression quantiles. Econometrica, 46, 33–50.

    Article  MathSciNet  MATH  Google Scholar 

  • Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5 (May)), 519–531.

    Article  Google Scholar 

  • Lee, Y.-S., Wollack, J. A., & Douglas, J. (2009). On the use of nonparametric item characteristic curve estimation techniques for checking parametric model fit. Educational and Psychological Measurement, 69(2 (April)), 181–197.

    MathSciNet  Google Scholar 

  • Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Adison-Wesley.

    MATH  Google Scholar 

  • Montanari, A., & Monari, P. (2005). Gini’s contribution to multivariate statistical analysis, Gini contribution to multivariate classification, regression trees. http://www.unisi.it/eventi/GiniLorenz05/paper%2026%20may/PAPER_Monari_Montanari.pdf.

  • O’Neill, D., & Van Kerm, P. (2008). An integrated framework for analysing income convergence. The Manchester School, 76(1 (January)), 1–20.

    Google Scholar 

  • Ramsay, J. O. (1995). A similarity-based smoothing approach to nondimensional item analysis. Psychometrika, 60, 323–339.

    Article  MATH  Google Scholar 

  • Rao, V. M. (1969). Two decompositions of concentration ratio. Journal of the Royal Statistical Society Series A (General), 132(3), 418–425.

    Article  MathSciNet  Google Scholar 

  • Schechtman, E., Soffer, E., & Yitzhaki, S. (2008). The robustness of conclusions based on TIMSS mean grades, first draft.

    Google Scholar 

  • Schechtman, E., Yitzhaki, S., & Pudalov, T. (2011). Gini’s multiple regressions: Two approaches and their interaction. Metron, LXIX(1), 65–97.

    Google Scholar 

  • Serfling, R. J. (1968). Contributions to central limit theory for dependent variables. The Annals of Mathematical Statistics, 39(8), 1158–1175.

    Article  MathSciNet  MATH  Google Scholar 

  • Serfling, R. J. (1980). Approximation theorems of mathematical statistics. New York: John Wiley and Sons.

    Book  MATH  Google Scholar 

  • Serfling, R. (2010). Autoregressive models via Yule-Walker equations allowing heavy tail innovations. Working paper. http://www.utdallas.edu/~serfling/papers/Serfling2010_AR_MR.pdf.

  • Shelef, A., & Schechtman, E. (2011). A Gini-based methodology for analyzing time series, draft. SSRN.com.

    Google Scholar 

  • Sijtsma, K., & Molenaar, I. W. (1987). Reliability of test scores in nonparametric item response theory. Psychmetrika, 52, 79–97.

    Article  MathSciNet  MATH  Google Scholar 

  • Simaan, Y. (1997). Estimation risk in portfolio selection: The mean variance model versus the mean absolute deviation model. Management Science, 43(10 (October)), 1437–1446.

    Article  Google Scholar 

  • Trajtenberg, M., & Yitzhaki, S. (1989). The diffusion of innovations: A methodological reappraisal. Journal of Business & Economic Statistics, 7(1 (January)), 35–47.

    Google Scholar 

  • Wainer, H., Gessaroli, M., & Verdi, M. (2006). Finding what is not there through the unfortunate binning of results: The Mendel effect. Chance, 19(1), 49–52.

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Yitzhaki, S. (1987). On the Relation between return and income. Quarterly Journal of Economics, 102(February), 77–95.

    Article  Google Scholar 

  • Yitzhaki, S., & Eisenstaedt, M. (2003). Ranking groups' versus individuals' ranking. In Y. Amiel & J. A. Bishop (Eds.), Fiscal policy, inequality, and welfare, research on economic inequality, 10 (pp. 101–123). Amsterdam: JAI.

    Chapter  Google Scholar 

  • Yitzhaki, S., & Olkin, I. (1988). Concentration curves. WP no. 179, Dept. of Economics, The Hebrew University and technical report no.230, 1987, Dept. of Statistics, Stanford University. http://statistics.stanford.edu/~ckirby/techreports/NSF/OLK%20NSF%20230.pdf.

  • Yitzhaki, S., & Schechtman, E. (2012). Identifying monotonic and non-monotonic relationships. Economics Letters, Economics Letters, 116, 23–25.

    Article  MathSciNet  MATH  Google Scholar 

  • Lord, F. M. (1970). Item characteristics curves estimated without knowledge of their mathematical form – A confrontation of Birnbaum’s logistic model. Psychometrika, 35, 43–50.

    Article  Google Scholar 

  • Lehmann, E. L. (1955). Ordered families of distributions. Annals of Mathematical Statistics, 26, 399–419.

    Article  MathSciNet  MATH  Google Scholar 

  • Spencer, B. D. (1983a). On interpreting test scores as social indicators: Statistical considerations. Journal of Educational Measurement, 20(4 (Winter)), 317–333.

    Article  Google Scholar 

  • Spencer, B. D. (1983b). Test scores as social statistics: Comparing distributions. Journal of Educational Statistics, 8, 249–269.

    Article  Google Scholar 

  • Yitzhaki, S., Itzhaki, R., & Pudalov, T. (2011). A nonparametric ICC using the Gini's mean difference approach. Unpublished, http://ssrn.com

  • Koenker, R., & Bassett, G. (1982). Robust tests for heteroscedasticity based on regression quantiles. Econometrica, 50, 43–61.

    Article  MathSciNet  MATH  Google Scholar 

  • Lord, F. M. (1980). Applications of Item Response Theory to Practical Testing Problems. Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.

    Google Scholar 

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edna Schechtman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Yitzhaki, S., Schechtman, E. (2013). Suggestions for Further Research. In: The Gini Methodology. Springer Series in Statistics, vol 272. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4720-7_23

Download citation

Publish with us

Policies and ethics

Search

Navigation