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Scrambling Reports: New Estimators for Estimating the Population Mean of Sensitive Variables

Author

Listed:
  • Pablo O. Juárez-Moreno

    (Higher School of Sociology, Universidad Autónoma de Guerrero, Acapulco 39310, Mexico)

  • Agustín Santiago-Moreno

    (Faculty of Mathematics, Universidad Autónoma de Guerrero, Acapulco 39650, Mexico)

  • José M. Sautto-Vallejo

    (Faculty of Mathematics, Universidad Autónoma de Guerrero, Acapulco 39650, Mexico)

  • Carlos N. Bouza-Herrera

    (Faculty of MATCOM, Universidad de La Habana, La Habana 11300, Cuba)

Abstract

Warner proposed a methodology called randomized response techniques, which, through the random scrambling of sensitive variables, allows the non-response rate to be reduced and the response bias to be diminished. In this document, we present a randomized response technique using simple random sampling. The scrambling of the sensitive variable is performed through the selection of a report R i , i = 1,2,3. In order to evaluate the accuracy and efficiency of the proposed estimators, a simulation was carried out with two databases, where the sensitive variables are the destruction of poppy crops in Guerrero, Mexico, and the age at first sexual intercourse. The results show that more accurate estimates are obtained with the proposed model.

Suggested Citation

  • Pablo O. Juárez-Moreno & Agustín Santiago-Moreno & José M. Sautto-Vallejo & Carlos N. Bouza-Herrera, 2023. "Scrambling Reports: New Estimators for Estimating the Population Mean of Sensitive Variables," Mathematics, MDPI, vol. 11(11), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2572-:d:1163557
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    References listed on IDEAS

    as
    1. Kuo-Chung Huang, 2008. "Estimation for sensitive characteristics using optional randomized response technique," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(5), pages 679-686, October.
    2. Ghulam Narjis & Javid Shabbir & Ronald Onyango & Tahir Mehmood, 2022. "Partial Randomized Response Model for Simultaneous Estimation of Means of Two Sensitive Variables," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-13, August.
    3. Carlos Bouza, 2009. "Ranked set sampling and randomized response procedures for estimating the mean of a sensitive quantitative character," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(3), pages 267-277, November.
    4. Zawar Hussain & Sidra Shakeel & Salman A. Cheema, 2022. "Estimation of stigmatized population total: A new additive quantitative randomized response model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(24), pages 8741-8753, December.
    5. Pier Francesco Perri & Beatriz Cobo Rodríguez & María del Mar Rueda García, 2018. "A mixed-mode sensitive research on cannabis use and sexual addiction: improving self-reporting by means of indirect questioning techniques," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1593-1611, July.
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