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

Abstract

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