On New Quantitative Randomized Response Techniques and a Weighted Privacy–Efficiency Measure

Shoaib Iqbal; Zawar Hussain

doi:10.64060/JASR2V2i3

Authors

Shoaib Iqbal Department of Statistics, Faculty of Computing, The Islamia University of Bahawalpur 63100, Pakistan Author https://orcid.org/0009-0002-2818-8220
Zawar Hussain Department of Statistics, Faculty of Computing, The Islamia University of Bahawalpur 63100, Pakistan Author https://orcid.org/0000-0002-5109-3652

DOI:

https://doi.org/10.64060/JASR2V2i3

Keywords:

Randomized response models, Scrambling models, Estimation of mean, Relative efficiency, Privacy protection

Abstract

Randomized response techniques are widely used for collecting information on sensitive variables while preserving respondent privacy. In the context of quantitative data, existing models are typically based on either additive or multiplicative scrambling mechanisms, which limit their flexibility in balancing estimation efficiency and privacy protection. This paper proposes a generalized class of quantitative randomized response models that integrates both additive and multiplicative components within a unified framework. From this formulation, three specific models (M₁- M₃) are developed, each representing a distinct configuration of the scrambling process and corresponding to different efficiency–privacy trade-offs. In addition, a weighted measure combining efficiency and privacy is introduced to facilitate a unified comparison of competing models. The proposed measure provides a flexible and interpretable criterion for model evaluation and supports consistent ranking under varying preference weights. Theoretical properties of the estimators are derived, and comparative analysis demonstrates the improved performance of the proposed models over existing techniques under a range of parameter settings. The proposed framework enhances the adaptability of randomized response methods and offers a practical tool for selecting appropriate models in sensitive survey applications.

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