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New scrambled response models for estimating the mean of a sensitive quantitative character

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  • Giancarlo Diana
  • Pier Francesco Perri

Abstract

Moving from the scrambling mechanism recently suggested by Saha [25], three scrambled randomized response (SRR) models are introduced with the intent to realize a right trade-off between efficiency and privacy protection. The models perturb the true response on the sensitive variable by resorting to the multiplicative and additive approaches in different ways. Some analytical and numerical comparisons of efficiency are performed to set up the conditions under which improvements upon Saha's model can be obtained and to quantify the efficiency gain. The use of auxiliary information is also discussed in a class of estimators for the sensitive mean under a generic randomization scheme. The class includes also the three proposed SRR models. Finally, some graphical comparisons are carried out from the double perspective of the accuracy in the estimates and respondents' privacy protection.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:11:p:1875-1890
    DOI: 10.1080/02664760903186031
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    References listed on IDEAS

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    1. Christopher Gjestvang & Sarjinder Singh, 2007. "Forced quantitative randomized response model: a new device," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 243-257, September.
    2. Shaul K. Bar-Lev & Elizabeta Bobovitch & Benzion Boukai, 2004. "A note on randomized response models for quantitative data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 255-260, November.
    3. 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.
    4. van den Hout, Ardo & van der Heijden, Peter G.M. & Gilchrist, Robert, 2007. "The logistic regression model with response variables subject to randomized response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6060-6069, August.
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    Citations

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    Cited by:

    1. Priyanka Kumari & Trisandhya Pidugu, 2019. "Modelling Sensitive Issues On Successive Waves," Statistics in Transition New Series, Statistics Poland, vol. 20(1), pages 41-65, March.
    2. María del Mar Rueda & Beatriz Cobo & Antonio Arcos, 2021. "Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    3. 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.
    4. Antonio Arcos & María del Rueda & Sarjinder Singh, 2015. "A generalized approach to randomised response for quantitative variables," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1239-1256, May.
    5. María del Mar García Rueda & Pier Francesco Perri & Beatriz Rodríguez Cobo, 2018. "Advances in estimation by the item sum technique using auxiliary information in complex surveys," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 455-478, July.
    6. 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.
    7. Kumari Priyanka & Pidugu Trisandhya & Richa Mittal, 2018. "Dealing sensitive characters on successive occasions through a general class of estimators using scrambled response techniques," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 203-230, August.
    8. Giancarlo Diana & Saba Riaz & Javid Shabbir, 2014. "Hansen and Hurwitz estimator with scrambled response on the second call," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 596-611, March.
    9. 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.
    10. Kumari Priyanka & Pidugu Trisandhya, 2019. "Modelling Sensitive Issues On Successive Waves," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 41-65, March.

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