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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    4. 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.
    5. 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.
    6. 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.
    7. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    8. 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.
    9. 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.
    10. 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.
    11. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    12. Thomas, Vinod & Wang, Yan & Fan, Xibo, 2001. "Measuring education inequality - Gini coefficients of education," Policy Research Working Paper Series 2525, The World Bank.
    13. 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.
    14. 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.
    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. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    4. 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.
    5. 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.
    6. 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.
    7. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics, Canadian Economics Association, vol. 43(4), pages 1122-1148, November.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Joan Costa-Font & Mireia Jofre-Bonet, 2013. "Anorexia, Body Image and Peer Effects: Evidence from a Sample of European Women," Economica, London School of Economics and Political Science, vol. 80(317), pages 44-64, January.
    13. Pérez, Carlos & Martín-Román, Ángel & Moral, Alfonso, 2020. "Two decades of the complementary leisure effect in Spain," The Journal of the Economics of Ageing, Elsevier, vol. 15(C).
    14. Huang, Qianqian & Jiang, Feng & Lie, Erik & Yang, Ke, 2014. "The role of investment banker directors in M&A," Journal of Financial Economics, Elsevier, vol. 112(2), pages 269-286.
    15. Wen-Hao Chen & Jean-Yves Duclos, 2011. "Testing for poverty dominance: an application to Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 44(3), pages 781-803, August.
    16. Ridhima Gupta, 2011. "Agro-environmental revolution in Punjab: Case of the happy seeder technology," Discussion Papers 11-11, Indian Statistical Institute, Delhi.
    17. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.
    18. Mehmet Pinar & Thanasis Stengos & M. Ege Yazgan, 2012. "Is there an Optimal Forecast Combination? A Stochastic Dominance Approach to Forecast Combination Puzzle," Working Paper series 17_12, Rimini Centre for Economic Analysis.
    19. Hsin-Fan Chen & Sheng-Hung Chen & Jie-Min Lee, 2024. "Does Risk Perception Endogenously Cause Smokers to Switch to Smoking Smuggled Cigarettes?," Studies in Microeconomics, , vol. 12(3), pages 296-307, December.
    20. François‐Charles Wolff & Ralitza Dimova, 2009. "Upstream Transfers And The Donor'S Labour Supply: Evidence From Migrants Living In France," Manchester School, University of Manchester, vol. 77(2), pages 204-224, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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: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.