Kernel Density Estimation for Joint Scrambling in Sensitive Surveys
Randomized response models aim to protect respondent privacy when sampling sensitive variables but consequently compromise estimator efficiency. We propose a new sampling method, titled joint scrambling, which preserves all true responses while protecting privacy by asking each respondent to jointly...
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MDPI AG
2025-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/13/2134 |
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| author | Alvan Caleb Arulandu Sat Gupta |
| author_facet | Alvan Caleb Arulandu Sat Gupta |
| author_sort | Alvan Caleb Arulandu |
| collection | DOAJ |
| description | Randomized response models aim to protect respondent privacy when sampling sensitive variables but consequently compromise estimator efficiency. We propose a new sampling method, titled joint scrambling, which preserves all true responses while protecting privacy by asking each respondent to jointly speak both their true response and multiple random responses in an arbitrary order. We give a kernel density estimator for the density function with asymptotically equivalent mean squared error for the optimal bandwidth yet greater generality than existing techniques for randomized response models. We also give consistent, unbiased estimators for a general class of estimands including the mean. For the cumulative distribution function, this estimator is more computationally efficient with asymptotically lower mean squared error than existing approaches. All results are verified via simulation and evaluated with respect to natural generalizations of existing privacy notions. |
| format | Article |
| id | doaj-art-a8c4d5a2d34b4874801e990dbe00ab39 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a8c4d5a2d34b4874801e990dbe00ab392025-08-20T03:50:16ZengMDPI AGMathematics2227-73902025-06-011313213410.3390/math13132134Kernel Density Estimation for Joint Scrambling in Sensitive SurveysAlvan Caleb Arulandu0Sat Gupta1Department of Mathematics, Harvard University, 33 Lowell Mail Center, 10 Holyoke Place, Cambridge, MA 02138, USADepartment of Mathematics and Statistics, University of North Carolina at Greensboro, 116 Petty Building, Greensboro, NC 27412, USARandomized response models aim to protect respondent privacy when sampling sensitive variables but consequently compromise estimator efficiency. We propose a new sampling method, titled joint scrambling, which preserves all true responses while protecting privacy by asking each respondent to jointly speak both their true response and multiple random responses in an arbitrary order. We give a kernel density estimator for the density function with asymptotically equivalent mean squared error for the optimal bandwidth yet greater generality than existing techniques for randomized response models. We also give consistent, unbiased estimators for a general class of estimands including the mean. For the cumulative distribution function, this estimator is more computationally efficient with asymptotically lower mean squared error than existing approaches. All results are verified via simulation and evaluated with respect to natural generalizations of existing privacy notions.https://www.mdpi.com/2227-7390/13/13/2134kernel density estimationprivacy protectionrandomized responsescramblingsensitive survey sampling |
| spellingShingle | Alvan Caleb Arulandu Sat Gupta Kernel Density Estimation for Joint Scrambling in Sensitive Surveys Mathematics kernel density estimation privacy protection randomized response scrambling sensitive survey sampling |
| title | Kernel Density Estimation for Joint Scrambling in Sensitive Surveys |
| title_full | Kernel Density Estimation for Joint Scrambling in Sensitive Surveys |
| title_fullStr | Kernel Density Estimation for Joint Scrambling in Sensitive Surveys |
| title_full_unstemmed | Kernel Density Estimation for Joint Scrambling in Sensitive Surveys |
| title_short | Kernel Density Estimation for Joint Scrambling in Sensitive Surveys |
| title_sort | kernel density estimation for joint scrambling in sensitive surveys |
| topic | kernel density estimation privacy protection randomized response scrambling sensitive survey sampling |
| url | https://www.mdpi.com/2227-7390/13/13/2134 |
| work_keys_str_mv | AT alvancalebarulandu kerneldensityestimationforjointscramblinginsensitivesurveys AT satgupta kerneldensityestimationforjointscramblinginsensitivesurveys |