Optimality of Ratio-Type Imputation Methods for Estimation of Population Mean Using Higher Order Moment of an Auxiliary Variable

This paper introduces some improved ratio methods of imputation using higher-order moment of an auxiliary variable while imputing missing values. It is well-known fact that the optimal ratio estimators attain the MSE of regression estimator, but while using Searls-type transformation this may not always happen. The performance of the proposed imputation methods is investigated relative to the methods proposed by Bhushan et al. (Commun Stat Simul Comput, 2018. https://doi.org/10.1080/03610918.2018.1500595), Mohamed et al. (Commun Stat Simul Comput, 2017. https://doi.org/10.1080/03610918.2016.1208235) and Bhushan and Pandey (J Stat Manag Syst 19(6):755-769, 2016, Commun Stat Theory Methods 47(11):2576-2589, 2018). A comparative study has been carried out, and it has been shown that the proposed methods perform better in comparison with methods proposed by Bhushan et al. (2018), Mohamed et al. (2017) and Bhushan and Pandey (2016, 2018). The theoretical findings are supported by numerical study on two real populations and a simulation study using hypothetical population.