IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1710.09009.html
   My bibliography  Save this paper

Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions

Author

Listed:
  • Fabian Dunker
  • Stephan Klasen
  • Tatyana Krivobokova

Abstract

Ratio of medians or other suitable quantiles of two distributions is widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated cross-sectional data are available. Inspired by the so-called growth incidence curves introduced in poverty research, we argue that the ratio of quantile functions is a more appropriate and informative tool to compare two distributions. We present an estimator for the ratio of quantile functions and develop corresponding simultaneous confidence bands, which allow to assess significance of certain features of the quantile functions ratio. Derived simultaneous confidence bands rely on the asymptotic distribution of the quantile functions ratio and do not require re-sampling techniques. The performance of the simultaneous confidence bands is demonstrated in simulations. Analysis of the expenditure data from Uganda in years 1999, 2002 and 2005 illustrates the relevance of our approach.

Suggested Citation

  • Fabian Dunker & Stephan Klasen & Tatyana Krivobokova, 2017. "Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions," Papers 1710.09009, arXiv.org.
    • Handle: RePEc:arx:papers:1710.09009
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1710.09009
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chesneau, Christophe & Dewan, Isha & Doosti, Hassan, 2016. "Nonparametric estimation of a quantile density function by wavelet methods," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 161-174.
    2. François Bourguignon, 2011. "Non-anonymous growth incidence curves, income mobility and social welfare dominance," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 605-627, December.
    3. Ravallion, Martin, 2004. "Pro-poor growth : A primer," Policy Research Working Paper Series 3242, The World Bank.
    4. Ravallion, Martin & Chen, Shaohua, 2003. "Measuring pro-poor growth," Economics Letters, Elsevier, vol. 78(1), pages 93-99, January.
    5. Michael Grimm, 2007. "Removing the anonymity axiom in assessing pro-poor growth," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(2), pages 179-197, August.
    6. M. Jones, 1992. "Estimating densities, quantiles, quantile densities and density quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 721-727, December.
    7. Grosse, Melanie & Harttgen, Kenneth & Klasen, Stephan, 2008. "Measuring Pro-Poor Growth in Non-Income Dimensions," World Development, Elsevier, vol. 36(6), pages 1021-1047, June.
    8. Einmahl, J. H. & Mason, D. M., 1988. "Strong limit theorems for weighted quantile processes," Other publications TiSEM 4bbe972d-b641-42a4-b2b8-0, Tilburg University, School of Economics and Management.
    9. Klasen, Stephan, 2008. "Economic Growth and Poverty Reduction: Measurement Issues using Income and Non-Income Indicators," World Development, Elsevier, vol. 36(3), pages 420-445, March.
    10. Francesca Dominici & Leslie Cope & Daniel Q. Naiman & Scott L. Zeger, 2005. "Smooth quantile ratio estimation," Biometrika, Biometrika Trust, vol. 92(3), pages 543-557, September.
    11. Soni, Pooja & Dewan, Isha & Jain, Kanchan, 2012. "Nonparametric estimation of quantile density function," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3876-3886.
    12. Francesca Dominici & Scott L. Zeger & Giovanni Parmigiani & Joanne Katz & Parul Christian, 2006. "Estimating percentile‐specific treatment effects in counterfactual models: a case‐study of micronutrient supplementation, birth weight and infant mortality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 261-280, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tomasz Panek, 2022. "Subjective Well-Being In European Union Countries," Working Papers 80, Institute of Statistics and Demography, Warsaw School of Economics.
    2. Tomasz Panek, 2019. "Czy wzrost gospodarczy w Polsce w latach 2005 -2015 był korzystny dla ubogich?," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 2, pages 5-39.
    3. B. Essama‐Nssah & Peter J. Lambert, 2009. "Measuring Pro‐Poorness: A Unifying Approach With New Results," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(3), pages 752-778, September.
    4. Higgins, Sean & Lustig, Nora, 2016. "Can a poverty-reducing and progressive tax and transfer system hurt the poor?," Journal of Development Economics, Elsevier, vol. 122(C), pages 63-75.
    5. Vito Peragine & Flaviana Palmisano & Paolo Brunori, 2014. "Economic Growth and Equality of Opportunity," The World Bank Economic Review, World Bank, vol. 28(2), pages 247-281.
    6. Flaviana Palmisano & Dirk Van de gaer, 2016. "History-dependent growth incidence: a characterization and an application to the economic crisis in Italy," Oxford Economic Papers, Oxford University Press, vol. 68(2), pages 585-603.
    7. Gbetoton Nadege Djossou & Gilles Quentin Kane & Jacob Novignon, 2017. "Is Growth Pro‐Poor in Benin? Evidence Using a Multidimensional Measure of Poverty," Poverty & Public Policy, John Wiley & Sons, vol. 9(4), pages 426-443, December.
    8. Sean Higgins & Nora Lustig, 2015. "Can Poverty-Reducing and Progressive Tax and Transfer System Hurt the Poor?," Commitment to Equity (CEQ) Working Paper Series 1333, Tulane University, Department of Economics.
    9. Khalid Zaman & Sadaf Shamsuddin, 2018. "Linear and Non-linear Relationships Between Growth, Inequality, and Poverty in a Panel of Latin America and the Caribbean Countries: A New Evidence of Pro-poor Growth," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(2), pages 595-619, April.
    10. Deutsch, Joseph & Silber, Jacques, 2011. "On various ways of measuring pro-poor growth," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-57.
    11. Stephan Klasen & Maria C. Lo Bue & Vincenzo Prete, 2020. "What's behind pro-poor growth?: The role of shocks and measurement error," WIDER Working Paper Series wp-2020-16, World Institute for Development Economic Research (UNU-WIDER).
    12. Buhong Zheng, 2011. "Consistent comparison of pro-poor growth," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 61-79, June.
    13. Alaa Mohamd Shoukry & Musarrat Jabeen & Khalid Zaman & Showkat Gani & Alamzeb Aamir, 2018. "A note on poverty, growth, and inequality nexus: evidence from a panel of sub-Saharan African countries," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(5), pages 2173-2195, September.
    14. Houngbonon, Georges Vivien & Bauer, Arthur & Ndiaye, Abdoulaye & Champagne, Clara & Yokossi, Tite, 2014. "Assessing the inclusiveness of growth in Africa: Evidence from Cameroon, Senegal, and Tanzania," WIDER Working Paper Series 120, World Institute for Development Economic Research (UNU-WIDER).
    15. Yonatan Berman & François Bourguignon, 2023. "On the social welfare interpretation of growth incidence curves," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(3), pages 723-741, September.
    16. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    17. Fourrier-Nicolaï Edwin & Lubrano Michel, 2024. "Bayesian inference for non-anonymous growth incidence curves using Bernstein polynomials: an application to academic wage dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 28(2), pages 319-336, April.
    18. Flaviana Palmisano, 2018. "Evaluating Patterns of Income Growth when Status Matters: A Robust Approach," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(1), pages 147-169, March.
    19. Jean-Pierre Lachaud, 2006. "La croissance pro-pauvres au Burkina Faso. L’éviction partielle de l’axiome d’anonymat en présence de données transversales," Documents de travail 126, Groupe d'Economie du Développement de l'Université Montesquieu Bordeaux IV.
    20. Kacem, Rami Ben Haj, 2013. "Monetary versus non-monetary pro-poor growth: Evidence from rural Ethiopia between 2004 and 2009," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 7, pages 1-22.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1710.09009. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.