Generalized Family of Estimators for Imputing Scrambled Responses

‎When there is a high correlation between the study and auxiliary variables‎, ‎the rank of the auxiliary variable also correlates with the study variable‎. ‎Then‎, ‎the use of the rank as an additional auxiliary variable may be helpful to increase the efficiency of the estimator of the mean or the total number of the population‎. ‎In the present study‎, ‎we propose two generalized families of estimators for imputing the scrambling responses by using the variance and the rank of the auxiliary variable‎. ‎Expressions for the bias and the mean squared error are obtained up to the first order of approximation‎. ‎A numerical study is carried out to observe the performance of estimators‎. ‎