Generalized Family of Estimators for Imputing Scrambled Re- sponses

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 useof the rank as an additional auxiliary variable may be helpful to increase the eciencyof the estimator of the mean or the total number of the population. in the presentstudy, we propose two generalized families of estimators for imputing the scramblingresponses by using the variance and the rank of the auxiliary variable. expressions forthe 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.