Modified Regression-Cum-Dual Mean Imputation Schemes for Estimating Population Mean Under Two-Phase Simple Random Sampling

Abstract

In sample survey methodology, the incorporation of auxiliary information at the 
estimation stage is widely recognized as an effective strategy for improving the 
precision of population parameter estimates. This study develops modified 
regression–cum–dual mean imputation estimators for the estimation of the 
population mean under a two-phase simple random sampling (SRS) framework. The 
proposed estimators integrate auxiliary variables within a regression-assisted 
imputation structure, combined with dual estimation principles, to enhance 
efficiency in the presence of incomplete data. The methodological formulation 
considers two distinct cases within the two-phase sampling design, allowing for 
flexibility in handling varying patterns of auxiliary information and missing 
observations. The proposed estimators are derived analytically, and their statistical 
properties are examined, with particular emphasis on bias and mean square error 
(MSE) as measures of estimator performance. Efficiency comparisons are conducted 
against selected existing estimators commonly applied in similar sampling contexts. 
The results demonstrate that the modified regression–cum–dual mean imputation 
estimators consistently achieve lower mean square errors relative to the competing 
estimators across both cases considered, indicating superior efficiency and 
improved precision in estimating the population mean. These findings underscore the 
robustness of the proposed approach and its suitability for practical applications in 
survey sampling where auxiliary information is available and missing data issues are 
present. Overall, the study contributes to the advancement of imputation-based 
estimation techniques by providing a more efficient class of estimators within the 
two-phase SRS framework.