An Enhanced Robust Type of Variance Estimator of Finite Population Variance

Abstract

Background: Sampling is the only approach suitable for obtaining the most accurate estimate of the population parameter under consideration if it is significant and it is time- and money-consuming to conduct observations on each population unit. For a more effective estimation of population variance, several authors have provided a variety of estimators.
Objective: The research aims to find an estimate of the population variance of the study variable that is more effective than the competing estimators.
Materials and Methods: The estimator has been created using data on the tri-mean, population correlation, interquartile range, First quartile of auxiliary variable, Third quartile, Quartile deviation, Population mid-range of auxiliary variable, Downton's Method, Gini's Mean Difference, Percentile of auxiliary variable etc. Up to the first level of approximation, the equations for the mean squared error (MSE) of the proposed estimator have been developed. The suggested estimator has been theoretically compared to the competing population variance estimators.
Results: The MSEs and PREs of the proposed and current estimators are shown in Table 2 using the aforementioned real-world dataset. Given that it has the lowest mean squared error of the competing population variance estimators, it has been determined that the suggested estimator is the best one.
Conclusion: The proposed estimator must be used for the improved estimate of population variance, as it is superior to competing estimators of population variance.