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Estimation of Gini Index within Pre-Specified Error Bound

Author

Listed:
  • Bhargab Chattopadhyay

    (Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080, USA)

  • Shyamal Krishna De

    (School of Mathematical Sciences, National Institute of Science Education and Research, Jatni 752050, Odisha, India)

Abstract

Gini index is a widely used measure of economic inequality. This article develops a theory and methodology for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width without assuming any specific distribution of the data. Fixed sample size methods cannot simultaneously achieve both specified confidence coefficient and fixed width. We develop a purely sequential procedure for interval estimation of Gini index with a specified confidence coefficient and a specified margin of error. Optimality properties of the proposed method, namely first order asymptotic efficiency and asymptotic consistency properties are proved under mild moment assumptions of the distribution of the data.

Suggested Citation

  • Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:3:p:30-:d:72720
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    References listed on IDEAS

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    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. Ransom, Michael R. & Cramer, Jan S., 1983. "Income distribution functions with disturbances," European Economic Review, Elsevier, vol. 22(3), pages 363-372.
    3. Paola Palmitesta & Corrado Provasi & Cosimo Spera, 2000. "Confidence Interval Estimation for Inequality Indices of the Gini Family," Computational Economics, Springer;Society for Computational Economics, vol. 16(1/2), pages 137-147, October.
    4. 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.
    5. 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.
    6. Barry C. Arnold, 2005. "Inequality measures for multivariate distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 317-327.
    7. 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.
    8. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    9. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
    10. Bishop, John A & Formby, John P & Zheng, Buhong, 1997. "Statistical Inference and the Sen Index of Poverty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 381-387, May.
    11. Bhattacharya, Debopam, 2005. "Asymptotic inference from multi-stage samples," Journal of Econometrics, Elsevier, vol. 126(1), pages 145-171, May.
    12. Matti Langel & Yves Tillé, 2013. "Variance estimation of the Gini index: revisiting a result several times published," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(2), pages 521-540, February.
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    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. 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.

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