An Improved Estimation Procedure of the Mean of a Sensitive Variable Using Auxiliary Information

Let Y be the variable under study, a sensitive variable which can’t be observed directly. Let X is a non – sensitive auxiliary variable which is strongly correlated with Y. Let S be a scrambling variable independent of the study variable Y and the auxiliary variable X. The usual additive model used for gathering information on quantitative sensitive variable is due to Himmelfarb & Edgell [3]. Their model allows the interviewee to hide personal information using a scrambling variable to their response. The respondent is asked to report a scrambled response for the study variable Y (based on additive model) given by Za =Y+S, but is asked to provided a true response for the auxiliary variable X [1].