New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable
A new randomized response technique for estimating the population total, or the population mean of a quantitative variable is proposed. It provides a high degree of protection to the respondents because they never report their data. Therefore, it may be favorably perceived by them and increase their...
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| Format: | Article |
| Language: | English |
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Czech Statistical Office
2022-06-01
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| Series: | Statistika: Statistics and Economy Journal |
| Subjects: | |
| Online Access: | https://www.czso.cz/documents/10180/167607757/32019722_205_antoch.pdf/a5b3898f-57ab-4938-8ae8-553f1277e55c?version=1.1 |
| _version_ | 1818249415240974336 |
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| author | Jaromír Antoch Francesco Mola Ondřej Vozár |
| author_facet | Jaromír Antoch Francesco Mola Ondřej Vozár |
| author_sort | Jaromír Antoch |
| collection | DOAJ |
| description | A new randomized response technique for estimating the population total, or the population mean of a quantitative variable is proposed. It provides a high degree of protection to the respondents because they never report their data. Therefore, it may be favorably perceived by them and increase their willingness to cooperate. Instead of revealing the true value of the characteristic under investigation, the respondent only states whether the value is greater (or smaller) than a number which is selected by him/her at random and is unknown to the interviewer. For each respondent, this number, a sort of individual threshold, is generated as a pseudorandom number. Furthermore, two modifications of the proposed technique are presented. The first modification assumes that the interviewer also knows the generated random number. The second modification deals with the issue that, for certain variables, such as income, it may be embarrassing for the respondents to report either high or low values. Thus, depending on the value of the fixed threshold (unknown to the respondent), the respondent is asked different questions to avoid being embarrassed. The suggested approach is applied in detail to the simple random sampling without replacement, but it can be, after a straightforward modification, applied to many sampling schemes, including cluster sampling, two-stage sampling, or stratified sampling. The results of the simulations illustrate the behavior of the proposed technique. |
| first_indexed | 2024-12-12T15:36:08Z |
| format | Article |
| id | doaj.art-7fe6ec995fb747e89ff0bafad61dbf0d |
| institution | Directory Open Access Journal |
| issn | 0322-788X 1804-8765 |
| language | English |
| last_indexed | 2024-12-12T15:36:08Z |
| publishDate | 2022-06-01 |
| publisher | Czech Statistical Office |
| record_format | Article |
| series | Statistika: Statistics and Economy Journal |
| spelling | doaj.art-7fe6ec995fb747e89ff0bafad61dbf0d2022-12-22T00:19:59ZengCzech Statistical OfficeStatistika: Statistics and Economy Journal0322-788X1804-87652022-06-01102220522710.54694/stat.2022.11New Randomized Response Technique for Estimating the Population Total of a Quantitative VariableJaromír Antoch0Francesco Mola1Ondřej Vozár2Charles University, Prague, Czech RepublicUniversit`a di Cagliari, Cagliari, ItalyPrague University of Economics and Business, Prague, Czech RepublicA new randomized response technique for estimating the population total, or the population mean of a quantitative variable is proposed. It provides a high degree of protection to the respondents because they never report their data. Therefore, it may be favorably perceived by them and increase their willingness to cooperate. Instead of revealing the true value of the characteristic under investigation, the respondent only states whether the value is greater (or smaller) than a number which is selected by him/her at random and is unknown to the interviewer. For each respondent, this number, a sort of individual threshold, is generated as a pseudorandom number. Furthermore, two modifications of the proposed technique are presented. The first modification assumes that the interviewer also knows the generated random number. The second modification deals with the issue that, for certain variables, such as income, it may be embarrassing for the respondents to report either high or low values. Thus, depending on the value of the fixed threshold (unknown to the respondent), the respondent is asked different questions to avoid being embarrassed. The suggested approach is applied in detail to the simple random sampling without replacement, but it can be, after a straightforward modification, applied to many sampling schemes, including cluster sampling, two-stage sampling, or stratified sampling. The results of the simulations illustrate the behavior of the proposed technique.https://www.czso.cz/documents/10180/167607757/32019722_205_antoch.pdf/a5b3898f-57ab-4938-8ae8-553f1277e55c?version=1.1survey samplingpopulation totalhorvitz-thompson´s estimatorrandomized response techniquessimple random sampling |
| spellingShingle | Jaromír Antoch Francesco Mola Ondřej Vozár New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable Statistika: Statistics and Economy Journal survey sampling population total horvitz-thompson´s estimator randomized response techniques simple random sampling |
| title | New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable |
| title_full | New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable |
| title_fullStr | New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable |
| title_full_unstemmed | New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable |
| title_short | New Randomized Response Technique for Estimating the Population Total of a Quantitative Variable |
| title_sort | new randomized response technique for estimating the population total of a quantitative variable |
| topic | survey sampling population total horvitz-thompson´s estimator randomized response techniques simple random sampling |
| url | https://www.czso.cz/documents/10180/167607757/32019722_205_antoch.pdf/a5b3898f-57ab-4938-8ae8-553f1277e55c?version=1.1 |
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