Detecting untruthful answering in randomized response sampling

This paper considers the problem of unbiasedly estimating the population proportion when the study variable is potential sensitive in nature. In order to protect the respondent's privacy, various techniques of generating randomized response rather than direct response are available in the literature. But the theory concerning them is developed only under the hypothesis of completely truthful reporting. Actually, the occurrence of untruthful reporting is a prospect in dealing with highly sensitive matters such as abortion or socially deviant behaviors. Illustrating Warner's [(1965), Journal of the American Statistical Association. 60: 63-69] randomized response technique we show how unbiased estimation of the population proportion can be extended to cover a case when some respondents may lie.