Generalized Family of Estimators for Imputing Scrambled Responses

When there is a high correlation between the study and the  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 total of the population.   In the present study, we propose two  generalized families of  estimators for imputing scrambling response by using the variance and rank of the auxiliary variable. Expressions for bias and mean squared error  are obtained up to the first order of approximation. A numerical study is carried out to observe the performance of estimators.