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Gini index estimation in randomized response surveys

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  • Lucio Barabesi
  • Giancarlo Diana
  • Pier Perri

Abstract

In this paper, we address the problem of estimating the Gini index when data are assumed to be collected through the randomized response method proposed by Greenberg et al. (J Am Stat Assoc 66:243–250 1971 ). In the design-based framework, we treat the Gini index as a population functional and follow the approach proposed by Deville (Surv Methodol 25:193–203 1999 ) to obtain the corresponding estimator. Variance estimation is also considered. A simulation study is carried out using real income data from the Survey of Household Income and Wealth conducted by the Bank of Italy ( 2010 ) in order to assess the performance of the proposed estimators. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Lucio Barabesi & Giancarlo Diana & Pier Perri, 2015. "Gini index estimation in randomized response surveys," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 45-62, January.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:1:p:45-62
    DOI: 10.1007/s10182-014-0230-8
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    References listed on IDEAS

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    1. Lucio Barabesi & Giancarlo Diana & Pier Perri, 2013. "Design-based distribution function estimation for stigmatized populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 919-935, October.
    2. Pier Perri & Peter Heijden, 2012. "A Property of the CHAID Partitioning Method for Dichotomous Randomized Response Data and Categorical Predictors," Journal of Classification, Springer;The Classification Society, vol. 29(1), pages 76-90, April.
    3. Stephen P. Jenkins & Richard V. Burkhauser & Shuaizhang Feng & Jeff Larrimore, 2011. "Measuring inequality using censored data: a multiple‐imputation approach to estimation and inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(1), pages 63-81, January.
    4. Giancarlo Diana & Pier Perri, 2011. "A class of estimators for quantitative sensitive data," Statistical Papers, Springer, vol. 52(3), pages 633-650, August.
    5. Raghunath Arnab & Sarjinder Singh, 2002. "Estimation of the Size and Mean Value of a Stigmatized Characteristic of a Hidden Gang in a Finite Population: A Unified Approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 659-666, September.
    6. repec:bla:obuest:v:62:y:2000:i:1:p:119-22 is not listed on IDEAS
    7. Matti Langel & Yves Tillé, 2012. "Inference by linearization for Zenga’s new inequality index: a comparison with the Gini index," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1093-1110, November.
    8. Lucio Barabesi & Marzia Marcheselli, 2010. "Bayesian estimation of proportion and sensitivity level in randomized response procedures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 75-88, July.
    9. Christopher R. Gjestvang & Sarjinder Singh, 2006. "A new randomized response model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 523-530, June.
    10. Giancarlo Diana & Pier Francesco Perri, 2012. "A calibration-based approach to sensitive data: a simulation study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 53-65, March.
    11. Giancarlo Diana & Pier Perri, 2009. "Estimating a sensitive proportion through randomized response procedures based on auxiliary information," Statistical Papers, Springer, vol. 50(3), pages 661-672, June.
    12. Lucio Barabesi & Sara Franceschi & Marzia Marcheselli, 2012. "A randomized response procedure for multiple-sensitive questions," Statistical Papers, Springer, vol. 53(3), pages 703-718, August.
    13. Sandstrom, Arne & Wretman, Jan H & Walden, Bertil, 1988. "Variance Estimators of the Gini Coefficient--Probability Sampling," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 113-119, January.
    14. Giancarlo Diana & Pier Francesco Perri, 2010. "New scrambled response models for estimating the mean of a sensitive quantitative character," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1875-1890.
    15. 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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    2. J. A. Mayor-Gallego & J. L. Moreno-Rebollo & M. D. Jiménez-Gamero, 2019. "Estimation of the finite population distribution function using a global penalized calibration method," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 1-35, March.

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