Efficient Optional Randomized Response Model for Estimating The Mean of a Sensitive Attribute with Known Sensitivity Level

I. B.  Okafor; A. C.  Onyeka; C. J.  Ogbonna; C. H.  Izunobi; F. C.  Okafor

doi:10.14419/03yt6271

Authors

I. B. Okafor Department of Statistics, Covenant Polytechnic, Aba, Abia State, Nigeria
A. C. Onyeka Department of Statistics, Federal University of Technology Owerri, Imo State, Nigeria
C. J. Ogbonna Department of Statistics, Federal University of Technology Owerri, Imo State, Nigeria
C. H. Izunobi Department of Statistics, Federal University of Technology Owerri, Imo State, Nigeria
F. C. Okafor Department of Statistics, University of Nigeria, Nsukka, Enugu State, Nigeria‎

DOI:

https://doi.org/10.14419/03yt6271

Published

08-02-2026

Keywords:

Mean; Privacy Protection; Scrambling Response; Sensitivity Level; Stochastic Disturbance

Abstract

The paper proposed an efficient optional randomized response model for estimating the mean of a sensitive variable with known sensitivity level. ‎The model introduced a multiplicative stochastic disturbance to further perturb respondents’ responses and offers the respondents the option to ‎either report a scrambled response or report a truthful response based on their perception of question sensitivity. Theoretical analysis confirms ‎that the estimator is unbiased with minimum variance compared to some existing models. Efficiency conditions and privacy metrics were ‎derived. The results of the empirical study show that the proposed model for different design parameter configurations recorded higher relative efficiency and privacy protection level. The log weighted privacy-efficiency measure further validates its robustness and practicality. By ‎and large, the model offers a reliable and flexible framework for collecting sensitive survey data while minimizing the response bias‎.

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