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 n x as an
estimate of X 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 2 S of
size n   1 nn is a subset of preliminary sample 1S   21SS , and
Case II: is when secondary sample 2 S is a subset of universal set 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.