An efficient estimator of population variance of a sensitive variable with a new randomized response technique
In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in exami...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844024035199 |
| _version_ | 1827316401621172224 |
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| author | Muhammad Azeem Najma Salahuddin Sundus Hussain Musarrat Ijaz Abdul Salam |
| author_facet | Muhammad Azeem Najma Salahuddin Sundus Hussain Musarrat Ijaz Abdul Salam |
| author_sort | Muhammad Azeem |
| collection | DOAJ |
| description | In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model. |
| first_indexed | 2024-04-24T23:13:52Z |
| format | Article |
| id | doaj.art-871f5c77ae884d3dbbbc1cc720e3a24e |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-24T23:13:52Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-871f5c77ae884d3dbbbc1cc720e3a24e2024-03-17T07:58:12ZengElsevierHeliyon2405-84402024-03-01105e27488An efficient estimator of population variance of a sensitive variable with a new randomized response techniqueMuhammad Azeem0Najma Salahuddin1Sundus Hussain2Musarrat Ijaz3Abdul Salam4Department of Statistics, University of Malakand, Khyber Pakhtunkhwa, Pakistan; Corresponding author.Department of Statistics, Shaheed Benazir Bhutto Women University, Peshawar, PakistanDepartment of Statistics, Shaheed Benazir Bhutto Women University, Peshawar, PakistanDepartment of Statistics, Rawalpindi Women University, Rawalpindi, PakistanDepartment of Statistics, University of Malakand, Khyber Pakhtunkhwa, PakistanIn sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model.http://www.sciencedirect.com/science/article/pii/S2405844024035199Auxiliary variableEfficiencyMean square errorRandomized response techniqueVariance estimator |
| spellingShingle | Muhammad Azeem Najma Salahuddin Sundus Hussain Musarrat Ijaz Abdul Salam An efficient estimator of population variance of a sensitive variable with a new randomized response technique Heliyon Auxiliary variable Efficiency Mean square error Randomized response technique Variance estimator |
| title | An efficient estimator of population variance of a sensitive variable with a new randomized response technique |
| title_full | An efficient estimator of population variance of a sensitive variable with a new randomized response technique |
| title_fullStr | An efficient estimator of population variance of a sensitive variable with a new randomized response technique |
| title_full_unstemmed | An efficient estimator of population variance of a sensitive variable with a new randomized response technique |
| title_short | An efficient estimator of population variance of a sensitive variable with a new randomized response technique |
| title_sort | efficient estimator of population variance of a sensitive variable with a new randomized response technique |
| topic | Auxiliary variable Efficiency Mean square error Randomized response technique Variance estimator |
| url | http://www.sciencedirect.com/science/article/pii/S2405844024035199 |
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