Estimation of finite Population mean in Non-response using Scrambled Response Model on second call

Abstract

This study is conducted to improve efficiency of the estimators of finite population mean in presence of non-response using Randomized Response Technique (RRT) to sub-sample non-respondents, assuming that non-response is due to sensitivity of the variable the variable under study. We suggest an estimator for the finite pop ulation mean incorporating known coefficient of variation of the study variable in case of quantitative sensitive variable considering a randomization mechanism on the second call that provides privacy protection to the respondents to get truthful information. We also propose generalized ratio and regression type estimators un der two-phase sampling. Secondly, we use stratified random sampling to improve efficiency of the propose estimators are derived. Expressions for mean square er ror of estimators are derived and conditions for which the proposed estimators are more efficient than the relevant estimators under scrambled response model have been obtained in case of simple random sampling and Stratified sampling. Numerical studies are carried out to evaluate performances of the estimators in both sampling schemes. Thirdly, we propose estimators in case of non-response using Ranked set sampling, Extreme Ranked set sampling and Median ranked set sampling to sub-sample non-respondents under randomized response model. Expressions for variances are obtain and conditions under which the proposed estimators are preferred on their counterpart in Simple random sampling with re placement. We conduct a monte carle experiment to see efficiency of the proposed estimators.