Regression estimator of population mean with random missing values in stratified two stage sampling using double sampling for auxiliary information

Abstract

Missing data is a recurring challenge in survey sampling, often reducing the efficiency and reliability of estimators. This study proposed and investigated the regression-type estimator of the population mean under a stratified two-stage sampling design in the presence of missing values. The population of the study comprised of Field survey data on students’ school attendance (auxiliary variable) and mathematics test scores (study variable). A stratified two-stage design was adopted, with schools as primary sampling units and students as secondary units. To reflect item nonresponse, 20% of the study variable was declared missing completely at random (MCAR) and handled through both regression and ratio imputation. The performance of the proposed regression estimator was compared with the Bahl-Saini (2011) ratio and difference estimator across sample sizes of 25, 40, 70, and 100, using coefficient of variation (CV), and confidence intervals as evaluation criteria. Results showed that the regression estimator consistently achieved lower variances and CVs than the existing estimators, with efficiency improving as sample size increased. Even in the presence of missing data, the regression estimator maintained superior performance, particularly under regression imputation. The study demonstrated the efficiency of the regression estimator in handling incomplete data and highlights its practical significance for reliable estimation in complex survey designs.