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A sampling estimator of the Bonferroni inequality index

Author

Listed:
  • Giovanni Maria Giorgi
  • Alessio Guandalini

    (Department of Statistical Sciences, �La Sapienza� University of Rome (Italy))

Abstract

A sampling estimator ( "B" ) of the Bonferroni inequality index based on the Bonferroni curve, is presented. "B" is compared through a simulation study with the percentile estimator and "B" , the estimator that uses weighted observations. It is shown that the "B" estimator, that decomposes the area between the Bonferroni curve and the line of perfect equality in trapezoids, has better performance than the other two, especially for small samples.

Suggested Citation

  • Giovanni Maria Giorgi & Alessio Guandalini, 2013. "A sampling estimator of the Bonferroni inequality index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 67(3-4), pages 151-158, July-Dece.
    • Handle: RePEc:ite:iteeco:133405
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    References listed on IDEAS

    as
    1. 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.
    2. Giovanni Maria Giorgi & Michele Crescenzi, 2005. "A look at the Bonferroni inequality measure in a reliability framework," Econometrics 0507004, University Library of Munich, Germany.
    3. Giovanni Maria Giorgi & Riccardo Mondani, 2005. "Sampling distribution of the Bonferroni inequality index from exponential population," Econometrics 0507008, University Library of Munich, Germany.
    4. Elena Bárcena-Martin & Jacques Silber, 2013. "On the generalization and decomposition of the Bonferroni index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 763-787, October.
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    Cited by:

    1. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
    2. Giovanni Maria Giorgi & Alessio Guandalini, 2016. "Bonferroni Index Decomposition And The Shapley Method," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 70(4), pages 67-78, October-D.
    3. Giovanni M. Giorgi & Alessio Guandalini, 2018. "Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality," Econometrics, MDPI, vol. 6(2), pages 1-16, April.
    4. Elena Bárcena-Martin & Jacques Silber, 2017. "The Bonferroni index and the measurement of distributional change," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 1-16, April.

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