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Estimation of Sensitive Attributes Using a Stratified Kuk Randomization Device
Estimación de atributos sensibles usando un mecanismo de aleatorización estratificado de Kuk
DOI:
https://doi.org/10.15446/rce.v40n1.53459Keywords:
Randomized response model, Kuk’s model, Sensitive attribute, Stratified sampling, Stratified double sampling (en)modelo Kuk ajustado, modelo de respuesta aleatorizada, atributos sensibles, muestreo doble estratificado, muestreo estratificado (es)
This paper suggests a stratified Kuk model to estimate the proportion of sensitive attributes of a population composed by a number of strata; this is undertaken by applying stratified sampling to the adjusted Kuk model. The paper estimates sensitive parameters when the size of the stratum is known by taking proportional and optimal allocation methods into account and then extends to the case of an unknown stratum size, estimating sensitive parameters by applying stratified double sampling and checking the two allocation methods. Finally, the paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the adjusted Kuk model in terms of the estimator variance.
Este trabajo propone un modelo Kuk estratificado para estimar la proporción de atributos sensibles de una población compuesta por varios estratos mediante la aplicación de un muestreo estratificado al modelo Kuk ajustado. El trabajo estima parámetros sensibles en el caso en que el tamaño del estrato es conocido mediante la adopción de métodos de asignación proporcionales y óptimos, y se extiende al caso de un tamaño de estrato desconocido, estimando parámetros sensibles mediante la aplicación de un doble muestreo estratificado y la comprobación de los dos métodos de asignación. Por último, el trabajo compara la eficiencia del modelo propuesto a la del modelo de Su, Sedory y Singh y el modelo Kuk ajustado en términos de la varianza del estimador.
https://doi.org/10.15446/rce.v40n1.53459
1Woosuk University, Department of Child Welfare, Wanju-gun Jeonbuk, Korea. PhD. Email: gisung@woosuk.ac.kr
2Dongshin University, Department of Computer Science, Naju Jeonnam country Korea. PhD. Email: khhong@dsu.ac.kr
3University of Minnesota at Morris, Division of Science and Mathematics, Statistics Discipline, Minnesota, USA. PhD. Email: jongmink@mrs.umn.edu
4Dongguk University, Department of Applied Statistics, Gyeongju Gyeongbuk, Republic of Korea. PhD. Email: ckson85@dongguk.ac.kr
This paper suggests a stratified Kuk model to estimate the proportion of sensitive attributes of a population composed by a number of strata; this is undertaken by applying stratified sampling to the adjusted Kuk model. The paper estimates sensitive parameters when the size of the stratum is known by taking proportional and optimal allocation methods into account and then extends to the case of an unknown stratum size, estimating sensitive parameters by applying stratified double sampling and checking the two allocation methods. Finally, the paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the adjusted Kuk model in terms of the estimator variance.
Key words: Adjusted Kuk Model, Randomized Response Model, Sensitive Attribute, Stratified Double Sampling, Stratified Sampling.
Este trabajo propone un modelo Kuk estratificado para estimar la proporción de atributos sensibles de una población compuesta por varios estratos mediante la aplicación de un muestreo estratificado al modelo Kuk ajustado. El trabajo estima parámetros sensibles en el caso en que el tamaño del estrato es conocido mediante la adopción de métodos de asignación proporcionales y óptimos, y se extiende al caso de un tamaño de estrato desconocido, estimando parámetros sensibles mediante la aplicación de un doble muestreo estratificado y la comprobación de los dos métodos de asignación. Por último, el trabajo compara la eficiencia del modelo propuesto a la del modelo de Su, Sedory y Singh y el modelo Kuk ajustado en términos de la varianza del estimador.
Palabras clave: modelo Kuk ajustado, modelo de respuesta aleatorizada, atributos sensibles, muestreo doble estratificado, muestreo estratificado.
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References
1. Chaudhuri, A. (2015), 'Fifty years gone by', Model Assisted Statistics and Applications 10(4), 277-282.
2. Chaudhuri, A. & Mukerjee, R. (1988), Randomized Response: Theory and Techniques, Marcel Dekker, Inc., New York.
3. Kim, J. M. & Elam, M. E. (2005), 'A Two-Stage stratified Warner's randomized Response Model Using Optimal Allocation', Metrika 61, 1-7.
4. Kim, J. M. & Warde, W. D. (2004), 'A stratified Warner's randomized response model', Journal of Statistical Planning and Inference 120, 155-165.
5. Kuk, A. Y. C. (1990), 'Asking sensitive questions indirectly', Biometrika 77, 436-438.
6. Ryu, J. B., Hong, K. H. & Lee, G. S. (1993), Randomized Response Model, Freedom Academy, Seoul.
7. Su, S. C., Sedory, S. A. & Singh, S. (2015), 'Kuk's model adjusted for protection and efficiency', Sociological Methods & Research 43(3), 534-551.
8. Tarray, T. & Singh, H. (2015), 'A randomized response model for estimating a rare sensitive attribute in stratified sampling using Poisson distribution', Model assisted Statistics & Applications 10(5), 361-384.
9. Warner, S. L. (1965), 'Randomized Response; A Survey Technique for Eliminating Evasive Answer Bias', Journal of the American Statistical Association 60, 63-69.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv40n1a02,
AUTHOR = {Gi-Sung, Lee and Ki-Hak, Hong and Jong-Min, Kim and Chang-Kyoon, Son},
TITLE = {{Estimation of Sensitive Attributes Using a Stratified Kuk Randomization Device}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2017},
volume = {40},
number = {1},
pages = {29-44}
}
References
Chaudhuri, A. (2015), ‘Fifty years gone by’, Model Assisted Statistics and Applications 10(4), 277–282.
Chaudhuri, A. & Mukerjee, R. (1988), Randomized Response: Theory and Techniques, Marcel Dekker, Inc., New York.
Kim, J. M. & Elam, M. E. (2005), ‘A Two-Stage stratified Warner’s randomized Response Model Using Optimal Allocation’, Metrika 61, 1–7.
Kim, J. M. & Warde, W. D. (2004), ‘A stratified Warner’s randomized response model’, Journal of Statistical Planning and Inference 120, 155–165.
Kuk, A. Y. C. (1990), ‘Asking sensitive questions indirectly’, Biometrika 77, 436–438.
Ryu, J. B., Hong, K. H. & Lee, G. S. (1993), Randomized Response Model, Freedom Academy, Seoul.
Su, S. C., Sedory, S. A. & Singh, S. (2015), ‘Kuk’s model adjusted for protection and efficiency’, Sociological Methods & Research 43(3), 534–551.
Tarray, T. & Singh, H. (2015), ‘A randomized response model for estimating a rare sensitive attribute in stratified sampling using Poisson distribution’, Model assisted Statistics & Applications 10(5), 361–384.
Warner, S. L. (1965), ‘Randomized Response; A Survey Technique for Eliminating Evasive Answer Bias’, Journal of the American Statistical Association 60, 63–69.
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