IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v79y2017i2d10.1007_s13571-017-0140-3.html
   My bibliography  Save this article

Minimum Risk Point Estimation of Gini Index

Author

Listed:
  • Shyamal K. De

    (National Institute of Science Education and Research, HBNI)

  • Bhargab Chattopadhyay

    (Indian Institute of Information Technology Vadodara
    University of Texas at Dallas)

Abstract

This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost at the same time. In this article, a purely sequential procedure is proposed which provides an estimate of the sample size required to achieve a sufficiently smaller estimation error and lower sampling cost. Characteristics of the purely sequential procedure are examined and asymptotic optimality properties are proved without assuming any specific distribution of the data. Performance of our method is examined through extensive simulation study.

Suggested Citation

  • Shyamal K. De & Bhargab Chattopadhyay, 2017. "Minimum Risk Point Estimation of Gini Index," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 247-277, November.
    • Handle: RePEc:spr:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0140-3
    DOI: 10.1007/s13571-017-0140-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-017-0140-3
    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/s13571-017-0140-3?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. William H. Greene, 1998. "Gender Economics Courses in Liberal Arts Colleges: Further Results," The Journal of Economic Education, Taylor & Francis Journals, vol. 29(4), pages 291-300, January.
    2. Lieven Wittebolle & Massimo Marzorati & Lieven Clement & Annalisa Balloi & Daniele Daffonchio & Kim Heylen & Paul De Vos & Willy Verstraete & Nico Boon, 2009. "Initial community evenness favours functionality under selective stress," Nature, Nature, vol. 458(7238), pages 623-626, April.
    3. Peter Arcidiacono & John Bailey Jones, 2003. "Finite Mixture Distributions, Sequential Likelihood and the EM Algorithm," Econometrica, Econometric Society, vol. 71(3), pages 933-946, May.
    4. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    5. Kuan Xu, 2007. "U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 567-577.
    6. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    7. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    8. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    9. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    10. Thomas, Vinod & Wang, Yan & Fan, Xibo, 2001. "Measuring education inequality - Gini coefficients of education," Policy Research Working Paper Series 2525, The World Bank.
    11. Kanninen Barbara J., 1993. "Design of Sequential Experiments for Contingent Valuation Studies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 1-11, July.
    12. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    13. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
    14. William Greene, 1998. "Gender Economics Courses in Liberal Arts Colleges: Comment," Working Papers 98-06, New York University, Leonard N. Stern School of Business, Department of Economics.
    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. Francis Bilson Darku & Frank Konietschke & Bhargab Chattopadhyay, 2020. "Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data," Econometrics, MDPI, vol. 8(2), pages 1-20, June.
    2. Ziqing Dong & Yves Tille & Giovanni Maria Giorgi & Alessio Guandalini, 2024. "Generalised Income Inequality Index," International Statistical Review, International Statistical Institute, vol. 92(1), pages 87-105, April.

    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. Francis Bilson Darku & Frank Konietschke & Bhargab Chattopadhyay, 2020. "Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data," Econometrics, MDPI, vol. 8(2), pages 1-20, June.
    2. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    3. Judith A. Clarke & Ahmed A. Hoque, 2014. "On Variance Estimation for a Gini Coefficient Estimator Obtained from Complex Survey Data," Econometrics Working Papers 1401, Department of Economics, University of Victoria.
    4. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    5. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics, Canadian Economics Association, vol. 43(4), pages 1122-1148, November.
    6. Bogdan Oancea & Dan Pirjol, 2019. "Extremal properties of the Theil and Gini measures of inequality," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(2), pages 859-869, March.
    7. Xuehua Yin & Narayanaswamy Balakrishnan & Chuancun Yin, 2023. "Bounds for Gini’s mean difference based on first four moments, with some applications," Statistical Papers, Springer, vol. 64(6), pages 2081-2100, December.
    8. Alfred Ultsch & Jörn Lötsch, 2017. "A data science based standardized Gini index as a Lorenz dominance preserving measure of the inequality of distributions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-15, August.
    9. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    10. Segol, Matthieu & Kolev, Atanas & Maurin, Laurent, 2021. "The impact of bank loan terms on intangible investment in Europe," EIB Working Papers 2021/05, European Investment Bank (EIB).
    11. Francesco Andreoli & Eugenio Peluso, 2016. "So close yet so unequal: Reconsidering spatial inequality in U.S. cities," Working Papers 21/2016, University of Verona, Department of Economics.
    12. Iain M. Cockburn & Megan J. MacGarvie, 2011. "Entry and Patenting in the Software Industry," Management Science, INFORMS, vol. 57(5), pages 915-933, May.
    13. Uwe Jirjahn & Jens Mohrenweiser & Stephen C Smith, 2022. "Works councils and workplace health promotion in Germany," Economic and Industrial Democracy, Department of Economic History, Uppsala University, Sweden, vol. 43(3), pages 1059-1094, August.
    14. Flachaire, Emmanuel & Nunez, Olivier, 2007. "Estimation of the income distribution and detection of subpopulations: An explanatory model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3368-3380, April.
    15. Francesco Andreoli & Eugenio Peluso, 2021. "Inference for the neighbourhood inequality index," Spatial Economic Analysis, Taylor & Francis Journals, vol. 16(3), pages 313-332, July.
    16. Chotikapanich, Duangkamon & Griffiths, William E, 2002. "Estimating Lorenz Curves Using a Dirichlet Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 290-295, April.
    17. ANDREOLI Francesco & PELUSO Eugenio, 2017. "So close yet so unequal: Spatial inequality in American cities," LISER Working Paper Series 2017-11, Luxembourg Institute of Socio-Economic Research (LISER).
    18. Vito Peragine & Laura Serlenga, 2008. "Higher education and equality of opportunity in Italy," Research on Economic Inequality, in: Inequality and Opportunity: Papers from the Second ECINEQ Society Meeting, pages 67-97, Emerald Group Publishing Limited.
    19. Blasch, Julia & Filippini, Massimo & Kumar, Nilkanth, 2019. "Boundedly rational consumers, energy and investment literacy, and the display of information on household appliances," Resource and Energy Economics, Elsevier, vol. 56(C), pages 39-58.
    20. Peter Arcidiacono & Paul B. Ellickson, 2011. "Practical Methods for Estimation of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 363-394, September.

    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:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0140-3. 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.