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Estimation of sample quantiles: challenges and issues in the context of income and wealth distributions
[Die Schätzung von Quantilen: Herausforderungen und Probleme im Kontext von Einkommens- und Vermögensverteilungen]

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  • Ann-Kristin Kreutzmann

    (Freie Universität Berlin)

Abstract

Means, quantiles and extreme values are common statistics for the description of distributions. However, estimating sample quantiles with the default definition in different software programs leads to unequal results. This is due to the fact that software programs use different quantile definitions. Since most practitioners are not aware of this fact and use different quantile definitions interchangeably, this work compares the default definitions in the software programs SPSS, R, SAS™ software, and Stata and additional quantile definitions that are suggested by the literature. The work especially focuses on how the quantile estimators perform in the context of describing the distribution of income and wealth. Furthermore, the possibilities of considering sampling weights in the quantile estimation and methods for producing variance estimates using the above-mentioned software are discussed.

Suggested Citation

  • Ann-Kristin Kreutzmann, 2018. "Estimation of sample quantiles: challenges and issues in the context of income and wealth distributions [Die Schätzung von Quantilen: Herausforderungen und Probleme im Kontext von Einkommens- und V," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(3), pages 245-270, December.
    • Handle: RePEc:spr:astaws:v:12:y:2018:i:3:d:10.1007_s11943-018-0234-z
    DOI: 10.1007/s11943-018-0234-z
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    1. Lumley, Thomas, 2004. "Analysis of Complex Survey Samples," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i08).
    2. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    3. K. Cheung & Stephen Lee, 2005. "Variance estimation for sample quantiles using them out ofn bootstrap," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 279-290, June.
    4. Arindam Chatterjee, 2011. "Asymptotic properties of sample quantiles from a finite population," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 157-179, February.
    5. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    6. repec:bla:jorssa:v:180:y:2017:i:4:p:1163-1190 is not listed on IDEAS
    7. Stefano Marchetti & Maciej Beręsewicz & Nicola Salvati & Marcin Szymkowiak & Łukasz Wawrowski, 2018. "The use of a three‐level M‐quantile model to map poverty at local administrative unit 1 in Poland," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1077-1104, October.
    8. Ralf Münnich & Jan Burgard & Martin Vogt, 2013. "Small Area-Statistik: Methoden und Anwendungen," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 6(3), pages 149-191, March.
    9. Stefano Marchetti & Caterina Giusti & Monica Pratesi, 2016. "The use of Twitter data to improve small area estimates of households’ share of food consumption expenditure in Italy [Die Nutzung von Twitter Daten um die Small Area Schätzungen vom Ausgabenanteil," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(2), pages 79-93, October.
    10. Alfons, Andreas & Templ, Matthias, 2013. "Estimation of Social Exclusion Indicators from Complex Surveys: The R Package laeken," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i15).
    11. Hans Walter Steinhauer & Christian Aßmann & Sabine Zinn & Solange Goßmann & Susanne Rässler, 2015. "Sampling and Weighting Cohort Samples in Institutional Contexts," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 9(2), pages 131-157, November.
    12. K. L. Majumder & G. P. Bhattacharjee, 1973. "The Incomplete Beta Integral," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 409-411, November.
    13. Jonas Beste & Markus M. Grabka & Jan Goebel, 2018. "Armut in Deutschland [Poverty in Germany]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(1), pages 27-62, April.
    14. Okolewski, Andrzej & Rychlik, Tomasz, 2001. "Sharp distribution-free bounds on the bias in estimating quantiles via order statistics," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 207-213, April.
    15. Yanyuan Ma & Marc Genton & Emanuel Parzen, 2011. "Asymptotic properties of sample quantiles of discrete distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 227-243, April.
    16. Monique Graf & Desislava Nedyalkova, 2014. "Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 821-842, December.
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