Novel efficient estimators of finite population mean in stratified random sampling with application

Abstract

Unbiased estimators are valuable when no auxiliary information is available beyond the primary study variables. However, once auxiliary information is accessible, biased estimators with smaller Mean Square Error (MSE) often outperform unbiased estimators that have large variances. We sought to develop new estimators that incorporate a single auxiliary variable in stratified random sampling. This study contributes to the field by introducing two distinct families of estimators designed to estimate the finite population mean. We conducted a theoretical evaluation of the estimators' performance by examining bias and MSE derived under first-order approximation. Additionally, we established the theoretical conditions necessary for the proposed estimator families to exhibit superior performance compared with existing alternatives. Empirical and simulation-based studies demonstrated significant improvements in estimators over competing estimators for finite-population parameter estimation.

Keywords

• unbiasedness
• auxiliary
• stratified random sampling
• efficiency
• mean square error