Aiding the well celebrated Kuk's randomized response technique through auxiliary and prior information

Abstract

Asking direct questions in face to face surveys about sensitive traits is an intricate issue. One of the solutions to this issue is the randomized response technique (RRT). Being the most widely used indirect questioning technique to obtain truthful data on sensitive traits in survey sampling RRT has been applied in a variety of fields including behavioral science, socio-economic, psychological, epidemiology, biomedical, criminology, data masking, public health engineering, conservation studies, ecological studies and many others. This paper aims at exploring the methods to subsidize the randomized response technique through additional information relevant to the parameter of interest. Specifically, we plan to contribute by proposing more efficient hybrid estimators compared to existing estimator based on (Kuk, 1990) [31] family of randomized response models. The proposed estimators are based on the methodology of incorporating the pertinent information, available on the basis of either historical records or expert opinion. Specifically, in case of availability of auxiliary information, the regression-cum-ratio estimator is found to be the best to further enhance the estimation through (Kuk, 1990) [31] model while the (Thompson, 1968) [49] shrinkage estimation is observed to be yielding more precise and accurate estimator of sensitive proportion. The findings in this study signify the importance of the proposed methodology. Additionally, to support the mathematical findings, a detailed numerical investigation to evaluate the comparative performances is also conducted. Based on performance analysis, overwhelming evidences are witnessed in the favor of proposed strategies.

Keywords

• Auxiliary variable
• Kuk design
• Randomized response techniques
• Sensitive attribute
• Shrinkage estimation procedures