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Testing Hypotheses About Absolute Concentration Curves And Marginal Conditional Stochastic Dominance

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  • Schechtman, Edna
  • Shelef, Amit
  • Yitzhaki, Shlomo
  • Zitikis, Ričardas

Abstract

We consider statistical tests concerning various relationships between two absolute concentration curves (ACCs). In particular, we consider tests for determining if the two ACCs coincide, if one is above another in a specified order, or if they do not intersect without specifying which one is above/below the other one. These problems are of interest in the context of marginal conditional stochastic dominance (MCSD). Constructing statistical tests for the MCSD relies on ideas and also on their modifications developed by Linton, Maasoumi, and Whang (2005, Review of Economic Studies 72, 735–765) in the context of stochastic dominance for distribution functions. Our theoretical considerations are supplemented with a simulation study.

Suggested Citation

  • Schechtman, Edna & Shelef, Amit & Yitzhaki, Shlomo & Zitikis, Ričardas, 2008. "Testing Hypotheses About Absolute Concentration Curves And Marginal Conditional Stochastic Dominance," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1044-1062, August.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:1044-1062_08
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    Cited by:

    1. Denuit, Michel M. & Huang, Rachel J. & Tzeng, Larry Y. & Wang, Christine W., 2014. "Almost marginal conditional stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 41(C), pages 57-66.
    2. Rolf Aaberge & Magne Mogstad, 2011. "Robust inequality comparisons," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 353-371, September.
    3. Khaled, Mohamad A. & Makdissi, Paul & Yazbeck, Myra, 2018. "Income-related health transfers principles and orderings of joint distributions of income and health," Journal of Health Economics, Elsevier, vol. 57(C), pages 315-331.
    4. Khadija Bchi & Paul Makdissi & Myra Yazbeck, 2024. "A modeling approach to decomposing changes in health concentration curves," Working Papers 2403E, University of Ottawa, Department of Economics.
    5. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
    6. Paul Makdissi & Myra Yazbeck, 2023. "Measuring the contribution of stratification and social class at birth to inequality of opportunity," Working Papers 2303E Classification- I31, University of Ottawa, Department of Economics.
    7. N. V. Gribkova & J. Su & R. Zitikis, 2022. "Empirical tail conditional allocation and its consistency under minimal assumptions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 713-735, August.
    8. Mohamad A. Khaled & Paul Makdissi & Myra Yazbeck, 2023. "On absolute socioeconomic health inequality comparisons," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 24(1), pages 5-25, February.
    9. 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.
    10. M. Grazia Pittau & Shlomo Yitzhaki & Roberto Zelli, 2011. "The make-up of a regression coefficient: An application to gender," DSS Empirical Economics and Econometrics Working Papers Series 2011/3, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    11. Doron Nisani & Amit Shelef, 2021. "A statistical analysis of investor preferences for portfolio selection," Empirical Economics, Springer, vol. 61(4), pages 1883-1915, October.
    12. Mohamad A. Khaled & Paul Makdissi & Myra Yazbeck, 2018. "On the importance of the upside down test in absolute socioeconomic health inequality comparisons," Discussion Papers Series 600, School of Economics, University of Queensland, Australia.
    13. Christopher J. Bennett, 2013. "Inference For Dominance Relations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(4), pages 1309-1328, November.
    14. Doron Nisani & Mahmoud Qadan & Amit Shelef, 2022. "Risk and Uncertainty at the Outbreak of the COVID-19 Pandemic," Sustainability, MDPI, vol. 14(14), pages 1-12, July.
    15. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    16. Edna Schechtman & Shlomo Yitzhaki & Taina Pudalov, 2011. "Gini’s multiple regressions: two approaches and their interaction," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-99.
    17. Zhidong Bai & Hua Li & Michael McAleer & Wing-Keung Wong, 2015. "Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 889-900, May.
    18. Greene Tom & Joffe Marshall & Hu Bo & Li Liang & Boucher Ken, 2013. "The Balanced Survivor Average Causal Effect," The International Journal of Biostatistics, De Gruyter, vol. 9(2), pages 291-306, May.

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