Adjusted variance estimators based on minimizing mean squared error for stratified random samples

In the realm of survey data analysis, encountering substantial variance relative to bias is a common occurrence. In this study, we present an innovative strategy to tackle this issue by introducing slightly biased variance estimators. These estimators incorporate a constant c within the range of 0 to 1, which is determined through the minimization of Mean Squared Error (MSE) for $ c \times (\hbox{variance estimator}) $ c×(variance estimator). This research builds upon the foundation laid by Kourouklis (2012, A new estimator of the variance based on minimizing mean squared error. The American Statistician, 66(4), 234–236) and extends their work into the domain of survey sampling. Extensive simulation studies are conducted to illustrate the superior performance of the adjusted variance estimators when compared to standard variance estimators, particularly in terms of MSE. These findings underscore the efficacy of our proposed approach in enhancing the precision of variance estimation within the context of survey data analysis.