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Some Calibration Estimators of the Mean of a Sensitive Variable Under Measurement Error

Author

Listed:
  • Sat Gupta

    (Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA)

  • Pidugu Trisandhya

    (Department of Applied Sciences, Bharati Vidyapeeth’s College of Engineering, New Delhi 110063, India)

  • Frank Coolen

    (Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK)

Abstract

This study explores the estimation of the mean of a sensitive variable using calibration estimators under measurement error. Three randomized response techniques are evaluated: Partial Randomized Response Technique, Compulsory Randomized Response Technique, and Optional Randomized Response Technique. Theoretical properties of the proposed estimators are analyzed, and a simulation study using real COVID-19 infection data is conducted. Results indicate that the Optional Randomized Response Technique outperforms Partial Randomized Response Technique and Compulsory Randomized Response Technique in terms of efficiency, underscoring its effectiveness and practical utility for improving data quality in sensitive survey settings.

Suggested Citation

  • Sat Gupta & Pidugu Trisandhya & Frank Coolen, 2025. "Some Calibration Estimators of the Mean of a Sensitive Variable Under Measurement Error," Mathematics, MDPI, vol. 13(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2532-:d:1719083
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    References listed on IDEAS

    as
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    5. Sanghamitra Pal, 2008. "Unbiasedly estimating the total of a stigmatizing variable from a complex survey on permitting options for direct or randomized responses," Statistical Papers, Springer, vol. 49(2), pages 157-164, April.
    6. James Abernathy & Bernard Greenberg & Daniel Horvitz, 1970. "Estimates of induced abortion in urban North Carolina," Demography, Springer;Population Association of America (PAA), vol. 7(1), pages 19-29, February.
    7. 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.
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