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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 5

Optimizing randomized response surveys: A new adaptive nonlinear scrambling approach for sensitive data collection

Tanveer Ahmad Tarray(Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India)0000-0003-4773-7151
Gazala Salam(Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India)0009-0000-3050-2288
Shuhrah Alghamdi(Princess Nourah bint Abdulrahman University, Riyadh 11564, Saudi Arabia)2345-6789-6567-7008
Danish Qayoom(Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune, India)0009-0006-0097-4288
Aafaq Rather(symbiosis Statistical Institute)0000-0001-8962-1660
Pages
—
Publication Date
2026-10-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A key innovation is an optimization framework that selects model parameters to minimize a combined efficiency–privacy metric, systematically enhancing overall performance.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study introduces an adaptive nonlinear optional randomized response technique that advances the trade-off between privacy and estimation efficiency in sensitive surveys.
📊
Key Findings & Data:A key innovation is an optimization framework that selects model parameters to minimize a combined efficiency–privacy metric, systematically enhancing overall performance.
💡
Conclusion & Impact:Consequently, an adaptive nonlinear optional randomized response technique emerges as a flexible, reliable tool for collecting sensitive data in education, social sciences, and public health, where respondent trust and data accuracy are paramount.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:Adaptive estimation · nonlinear scrambling · randomized response technique

Abstract

This study introduces an adaptive nonlinear optional randomized response technique that advances the trade-off between privacy and estimation efficiency in sensitive surveys. The model employs a nonlinear transformation function and a beta-distributed scrambling variable, allowing the perturbation mechanism to adapt dynamically to each question’s inherent sensitivity. This adaptability ensures stronger privacy guarantees without proportionally sacrificing the accuracy of population estimates. Theoretical derivations confirm the estimator’s unbiasedness, while also quantifying its improved variance and a robust privacy measure. A key innovation is an optimization framework that selects model parameters to minimize a combined efficiency–privacy metric, systematically enhancing overall performance. Validation through extensive simulation, a comprehensive survey of randomized response techniques for data privacy, and a data illustration show that an adaptive nonlinear optional randomized response Technique achieves significant reductions in estimator variance and gains in perceived privacy protection across a wide range of sensitivity probabilities. Compared to conventional optional randomized response techniques, it provides superior, balanced performance. Consequently, an adaptive nonlinear optional randomized response technique emerges as a flexible, reliable tool for collecting sensitive data in education, social sciences, and public health, where respondent trust and data accuracy are paramount.

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Cite This Article

Tarray, T. A., Salam, G., Alghamdi, S., Qayoom, D., Rather, A. (2026). Optimizing randomized response surveys: A new adaptive nonlinear scrambling approach for sensitive data collection. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 5. https://doi.org/10.15672/hujms.1891414

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References (35)

  1. S. L. Warner, Randomized response: A survey technique for eliminating evasive answer bias, J. Amer. Stat. Ass. 60 (309), 63–69, 1965.
  2. B. G. Greenberg, A.-L. A. Abul-Ela, W. R. Simmons and D. G. Horvitz, The unrelated question randomized response model: Theoretical framework, J. Amer. Stat. Ass. 64 (326), 520–539, 1969.
  3. B. H. Eichhorn and L. S. Hayre, Scrambled randomized response methods for obtaining sensitive quantitative data, J. Stat. Plan. and Infer. 7 (4), 307–316, 1983.
  4. S. K. Bar-Lev, E. Bobovitch and B. Boukai, A note on randomized response models for quantitative data, Metrika, 60 (3), 255–260, 2004.
  5. S. Gupta, B. Gupta, and S. Singh, Estimation of sensitivity level of personal interview survey questions, J. Stat. Plan. and Infer. 100 (2), 239–247, 2002.
  6. G. Diana and P. F. Perri, New scrambled response models for estimating the mean of a sensitive quantitative character, J. Appl.Stat. 37 (11), 1875–1890, 2010.
  7. G. Diana and P. F. Perri, A class of estimators of quantitative sensitive data Stat. Papers 52 (3), 653–660, 2011.
  8. C. R. Gjestvang and S. Singh, An improved randomized response model: Estimation of mean, J. App. Stat. 36 (12), 1361–1367, 2009.
  9. O. Odumade and S. Singh, An alternative to the Bar-Lev, Bobovitch and Boukai randomized response model, Socio. Meth. Res. 39 (2), 206–221, 2010.
  10. A. Saha, A simple randomized response technique in complex surveys, Metron 65 (1), 59–66, 2007.
  11. A. Saha, A randomized response technique for quantitative data under unequal probability sampling, J. Stat. Theo. Prac. 2 (4), 589–596, 2008.
  12. Z. Yan, J. Wang and J. Lai, An efficiency and protection degree based comparison among quantitative randomized response strategies, Com. Stat. Theo. Meth. 38 (3), 400–408, 2009.
  13. S. Gupta, J. Shabbir, S. Mehta and S. Khalil, A unified measure of respondent privacy and model efficiency in quantitative RRT models, J. Stat. Theo. Prac. 12 (3), 506–511, 2018.
  14. G. Najira and J. Shabbir, An efficient new scrambled response model for estimating sensitive population mean in successive sampling, Com. Stat. Simu. Comp. 50 (12), 3915–3932, 2021.
  15. H. P. Singh and S. M. Gorey, A remark on Gupta, Gupta and Singh optional randomized response model, J. Appl. Math. Stat. Infor. 15 (1), 43–73, 2019.
  16. A. A. Rather and C. Subramanian, A new exponentiated distribution with engineering science applications, J. Stat. App. Proba. 9 (1), 127-137, 2020.
  17. B. Singh, I. Alam, A. A. Rather and M. Alam Linear combination of order statistics of exponentiated Nadarajah–Haghighi distribution and their applications, Lob. J. Math. 44 (11), 4839–4848, 2023.
  18. A. A. Rather, M. Azeem, M. Alam, C. Subramanian, G. Ozel, and I. Ali, Weighted Erlang-truncated exponential distribution: System reliability optimization, structural properties, and simulation, Lob. J. Math. 45 (9), 4311-4337, 2024.
  19. A. Ahmad, Y. Tashkandy, A. A. Rather, M. E. Bakr, E. Hussam and A. M. Gemeay, Novel family of probability generating distributions: Properties and data analysis, Phy. Scri. 99 (12), 1-19, 2024.
  20. E. S. Alotaibi, N. E. Alsubaie, D. Qayoom, and A. A. Rather, A novel extension of Burhan distribution: Theoretical properties, simulation study and practical application, Lob. J. Math. 45 (12), 6224–6243, 2024.
  21. A. Ahmad, N. Alsadat, A. A. Rather, M. A. Meraou and M. M. Mohie El-Din, A novel statistical approach to covid-19 variability using the Weibull-inverse Nadarajah- Haghighi distribution, Alex. Eng. J. 105 (12), 950-962, 2024.
  22. A. Rashid, Z. Ahmad, A. A. Rather, and I. Ali, A note on class of Weibull–Pareto distribution, Lob. J. Math. 45 (2), 819–824, 2024.
  23. A. Ahmad, A. A. Rather, O. A. Alqasem, M. E. Bakr, G. T. Mekiso, O. S. Balogun, E. Hussam and A. M. Gemeay, Introducing novel arc cosine-ψ class of distribution with theory and data evaluation related to coronavirus, Sci. Rep. 15,13069, 1-23, 2025.
  24. D. Qayoom, A. A. Rather, O. A. Alqasem, Z. Ahmad, M. Nagy, A. M. Yousuf, A. H. Mansi, E. Hussam, and A. M. Gemeay, Development of a novel extension of Rayleigh distribution with application to covid-19 data, Sci. Rep. 15, 18535, 1-28 2025.
  25. A. A. Rather, A. R. El-Saeed, D. Qayoom, Z. Ahmad, H. E. Semary, G. T. Mekiso, E. Hussam and A. M. Gemeay, Quality assurance through truncated life tests under the Lomax distribution, Sci. Rep. 15, 24822, 2025.
  26. D. Qayoom, A. A. Rather and M. Alam, Length biased Burhan distribution: Properties, simulation and applications, Lob. J. Math. 46, 1374–1390, 2025.
  27. D. Qayoom, A. A. Rather, E. S. Alotaibi, B. A. Shukr, and A. A. Almazmomi, A novel extension of the power Lindely distribution with statistical properties and application to COVID-19 data, Sci. Rep. 15, 30486, 2025.
  28. M. M. Rueda, B. Cobo, and F. López-Torrecillas, Measuring inappropriate sexual behavior among university students: Using the randomized response technique to enhance self-reporting, Sex. Abu. 31 (4), 385–399, 2019.
  29. M. A. Yunusa and A. Adejumobi, Some log type estimators of population mean of sensitive variable using additive scrambling model, Orien. J. Phy. Sci. 9 (2), 1–10, 2024.
  30. M. A. Yunusa, A. Audu and A. Adejumobi, Robust optional randomized response technique models (RORRT) for seeking information about sensitive issues, Int. J. Sci. Res. Math. Stat. Sci. 12 (3), 1–7, 2025.
  31. A. A. Alafara, I. A. Imam and M. A. Yunusa, Improved logarithmic product cum ratio-type estimators for population coefficient of variation using known power transformation, Int. J. Sci. Res. Math. Stat. Sci. 12 (2), 56–64, 2025.
  32. A. A. Alafara, A. A. Opeyemi and A. A. Olamilekan, Improved generalized exponential ratio-cum-product estimator for estimating population variance under simple random sampling, Int. J. Sci. Res. Math. Stat. Sci. 12 (2), 77–85, (2025).
  33. A. A. Alafara, I. A. Imam and M. A. Yunusa, A study of the effect of measurement errors on improved finite population mean, Int. J. Sci. Res. Math. Stat. Sci. 12 (2), 136–145, 2025.
  34. F. W. Leysieffer and S. L. Warner, Respondent jeopardy and optimal designs in randomized response models, J. Amer. Stat. Asso. 71 (355), 649–656, 1976.
  35. S. Himmelfarb and S. E. Edgell, Additive constants model: A randomized response technique for eliminating evasiveness to quantitative response questions, Psy. Bull. 87 (3), 525–530, 1980.