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The relationship between the absolute deviation from a quantile and Gini’s mean difference

  • Shlomo Yitzhaki

    ()

  • Peter Lambert

    ()

We investigate the relationship between Gini’s mean difference (GMD), the mean absolute deviation, the least absolute deviation and the absolute deviation from a quantile. The latter can all be interpreted as equivalents either to the GMD of a transformed distribution or to a between-group GMD measure, according to the particular partition of the data. They all possess properties of the GMD but each omits the intra-group variability—and they give rise to different regression techniques. We argue that the analyst using one of these techniques should justify the omission of the intra-group variability from the analysis. Copyright Sapienza Università di Roma 2013

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File URL: http://hdl.handle.net/10.1007/s40300-013-0015-y
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Article provided by Springer in its journal METRON.

Volume (Year): 71 (2013)
Issue (Month): 2 (September)
Pages: 97-104

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Handle: RePEc:spr:metron:v:71:y:2013:i:2:p:97-104
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  1. Yusif Simaan, 1997. "Estimation Risk in Portfolio Selection: The Mean Variance Model Versus the Mean Absolute Deviation Model," Management Science, INFORMS, vol. 43(10), pages 1437-1446, October.
  2. repec:cup:cbooks:9780521845731 is not listed on IDEAS
  3. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  4. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
  5. Yitzhaki, Shlomo, 2002. "Do we need a separate poverty measurement?," European Journal of Political Economy, Elsevier, vol. 18(1), pages 61-85, March.
  6. Pakes, Ariel, 1982. "On the Asymptotic Bias of Wald-Type Estimators of a Straight Line When Both Variables Are Subject to Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 491-97, June.
  7. repec:cup:cbooks:9780521608275 is not listed on IDEAS
  8. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
  9. Frick, Joachim R. & Goebel, Jan & Schechtman, Edna & Wagner, Gert G. & Yitzhaki, Shlomo, 2004. "Using Analysis of Gini (ANoGi) for Detecting Whether Two Sub-Samples Represent the Same Universe: The SOEP Experience," IZA Discussion Papers 1049, Institute for the Study of Labor (IZA).
  10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  11. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
  12. Schechtman, E. & Yitzhaki, S., 1999. "On the proper bounds of the Gini correlation," Economics Letters, Elsevier, vol. 63(2), pages 133-138, May.
  13. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
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