Published

2017-01-16

Estimation of Sensitive Attributes Using a Stratified Kuk Randomization Device

Estimación de atributos sensibles usando un mecanismo de aleatorización estratificado de Kuk

Keywords:

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)

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Authors

  • Jong-Min Kim University of Minnesota at Morris
  • Gi-Sung Lee Woosuk University
  • Ki-Hak Hong Dongshin University
  • Chang-Kyoon Son Dongguk University- Gyeongju

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.

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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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