IDEAS home Printed from https://ideas.repec.org/a/spr/astaws/v12y2018i3d10.1007_s11943-018-0234-z.html
   My bibliography  Save this article

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]

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11943-018-0234-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11943-018-0234-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Lumley, Thomas, 2004. "Analysis of Complex Survey Samples," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i08).
    12. 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.
    13. Timo Schmid & Fabian Bruckschen & Nicola Salvati & Till Zbiranski, 2017. "Constructing sociodemographic indicators for national statistical institutes by using mobile phone data: estimating literacy rates in Senegal," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1163-1190, October.
    14. 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).
    15. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Timo Schmid & Markus Zwick, 2018. "Vorwort der Herausgeber," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(3), pages 189-193, December.

    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. Enrico Fabrizi & Maria Rosaria Ferrante & Carlo Trivisano, 2020. "A functional approach to small area estimation of the relative median poverty gap," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1273-1291, June.
    2. Patrick Krennmair & Timo Schmid, 2022. "Flexible domain prediction using mixed effects random forests," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1865-1894, November.
    3. Walter, Paul & Weimer, Katja, 2018. "Estimating poverty and inequality indicators using interval censored income data from the German microcensus," Discussion Papers 2018/10, Free University Berlin, School of Business & Economics.
    4. 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.
    5. Mathias Silva, 2023. "Parametric models of income distributions integrating misreporting and non-response mechanisms," AMSE Working Papers 2311, Aix-Marseille School of Economics, France.
    6. Duangkamon Chotikapanich & William E. Griffiths & Gholamreza Hajargasht & Wasana Karunarathne & D. S. Prasada Rao, 2018. "Using the GB2 Income Distribution," Econometrics, MDPI, vol. 6(2), pages 1-24, April.
    7. Marchetti Stefano & Tzavidis Nikos, 2021. "Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas," Journal of Official Statistics, Sciendo, vol. 37(4), pages 955-979, December.
    8. Nora Würz & Timo Schmid & Nikos Tzavidis, 2022. "Estimating regional income indicators under transformations and access to limited population auxiliary information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1679-1706, October.
    9. Tzavidis, Nikos & Zhang, Li-Chun & Luna Hernandez, Angela & Schmid, Timo & Rojas-Perilla, Natalia, 2016. "From start to finish: A framework for the production of small area official statistics," Discussion Papers 2016/13, Free University Berlin, School of Business & Economics.
    10. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    11. Louis Chauvel, 2014. "The Intensity and Shape of Inequality: The ABG Method of Distributional Analysis," LIS Working papers 609, LIS Cross-National Data Center in Luxembourg.
    12. Mathias Silva, 2023. "Parametric estimation of income distributions using grouped data: an Approximate Bayesian Computation approach [Working Papers / Documents de travail]," Working Papers hal-04066544, HAL.
    13. Louis Chauvel, 2016. "The Intensity and Shape of Inequality: The ABG Method of Distributional Analysis," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(1), pages 52-68, March.
    14. Jan Breitkreuz & Gabriela Brückner & Jan Pablo Burgard & Joscha Krause & Ralf Münnich & Helmut Schröder & Katrin Schüssel, 2019. "Schätzung kleinräumiger Krankheitshäufigkeiten für die deutsche Bevölkerung anhand von Routinedaten am Beispiel von Typ-2-Diabetes [Estimation of regional diabetes type 2 prevalence in the German p," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 13(1), pages 35-72, April.
    15. Till Koebe & Alejandra Arias‐Salazar & Natalia Rojas‐Perilla & Timo Schmid, 2022. "Intercensal updating using structure‐preserving methods and satellite imagery," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 170-196, December.
    16. Kreutzmann, Ann-Kristin & Marek, Philipp & Salvati, Nicola & Schmid, Timo, 2019. "Estimating regional wealth in Germany: How different are East and West really?," Discussion Papers 35/2019, Deutsche Bundesbank.
    17. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    18. Jos'e Miguel Flores-Contr'o, 2024. "The Gerber-Shiu Expected Discounted Penalty Function: An Application to Poverty Trapping," Papers 2402.11715, arXiv.org.
    19. Jan Pablo Burgard & Ralf Münnich & Martin Rupp, 2019. "A Generalized Calibration Approach Ensuring Coherent Estimates with Small Area Constraints," Research Papers in Economics 2019-10, University of Trier, Department of Economics.
    20. Duangkamon Chotikapanich & William E. Griffiths & Gholamreza Hajargasht & Wasana Karunarathne & D.S. Prasada Rao, 2018. "Using the GB2 Income Distribution: A Review," Department of Economics - Working Papers Series 2036, The University of Melbourne.

    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:spr:astaws:v:12:y:2018:i:3:d:10.1007_s11943-018-0234-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.