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Composing the cumulative quantile regression function and the Goldie concentration curve


  • Tse, SzeMan


The model we discuss in this paper deals with inequality in distribution in the presence of a covariate. To elucidate that dependence, we propose to consider the composition of the cumulative quantile regression (CQR) function and the Goldie concentration curve, the standardized counterpart of which gives a fraction to fraction plot of the response and the covariate. It has the merit of enhancing the visibility of inequality in distribution when the latter is present. We shall examine the asymptotic properties of the corresponding empirical estimator. The associated empirical process involves a randomly stopped partial sum process of induced order statistics. Strong Gaussian approximations of the processes are constructed. The result forms the basis for the asymptotic theory of functional statistics based on these processes.

Suggested Citation

  • Tse, SzeMan, 2011. "Composing the cumulative quantile regression function and the Goldie concentration curve," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 674-682, March.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:674-682

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    References listed on IDEAS

    1. Rao, C. R., 1995. "Strassen's Law of the Iterated Logarithm for the Lorenz Curves," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 239-252, August.
    2. Csörgo, Miklós & Zitikis, Ricardas, 1996. "Strassen's LIL for the Lorenz Curve," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 1-12, October.
    3. Schechtman, Edna & Shelef, Amit & Yitzhaki, Shlomo & Zitikis, RiÄ ardas, 2008. "Testing Hypotheses About Absolute Concentration Curves And Marginal Conditional Stochastic Dominance," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1044-1062, August.
    4. Csörgö, Miklós & Zitikis, Ricardas, 1997. "On the rate of strong consistency of Lorenz curves," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 113-121, June.
    5. Sze-Man Tse, 2006. "Lorenz Curve for Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 675-686, December.
    6. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    7. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
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    Cited by:

    1. Bosco, Bruno, 2019. "One size does not fit all: Quantile regression estimates of cross-country risk of poverty in Europe," Economic Analysis and Policy, Elsevier, vol. 62(C), pages 280-299.


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