Authors

• Muhammad Umair Sohail ¹
• Shabbir Javid ¹
• ‎Cem Kadilar ²
• Shakeel Ahmed ¹

¹ Department of Statistics‎, ‎Quaid-i-Azam University‎, ‎Islamabad‎, ‎Pakistan

² Department of Statistics‎, ‎Hacettepe University‎, ‎Beytepe‎, ‎Ankara‎, ‎Turkey

Abstract

‎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. ‎

Keywords

• Higher order moments‎
• ‎Imputation‎
• ‎Missing data‎
• ‎Scrambled responses‎
• ‎Sensitive attribute‎