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Hansen and Hurwitz estimator with scrambled response on the second call

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  • Giancarlo Diana
  • Saba Riaz
  • Javid Shabbir

Abstract

In this paper we propose a modified version of the estimator of Hansen and Hurwitz [12] in the case of quantitative sensitive variable and consider a randomization mechanism on the second call that provides privacy protection to the respondents to get truthful information. We use variance of the modified estimator as a tool to measure privacy protection and it is observed that the higher is the variance, the lower is the efficiency but the higher is the privacy protection. To overcome this efficiency loss, we consider a linear regression estimator using known non-sensitive auxiliary information. With consideration of four scrambled models, we try to make a trade-off between efficiency and privacy protection. To show this compromise, analytical and numerical comparisons are obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:3:p:596-611
    DOI: 10.1080/02664763.2013.846305
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    References listed on IDEAS

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    1. Housila Singh & Sunil Kumar, 2010. "Estimation of mean in presence of non-response using two phase sampling scheme," Statistical Papers, Springer, vol. 51(3), pages 559-582, 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. Giancarlo Diana & Marco Giordan & Pier Perri, 2011. "An improved class of estimators for the population mean," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 123-140, June.
    4. 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.
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    Cited by:

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