On the efficiency of modified regression-type mean imputation scheme under two-phase sampling

Human-based surveys such as medical and social science are often characterized by non-response or missing observations. In this study, a new class of regression-type mean imputation method that uses X̄n an estimate X̄ was suggested. Using partial derivative approach, the MSEs estimators presented were derived up to first order approximation under two cases. Case I: when secondary sample S2 size n(n<n1) is subset preliminary S1[S2 ⸦ S1] , II: universal set ΩN . Conditions for which estimator more efficient than other studied derived. The results numerical examples through simulations revealed suggested efficient.