Generalised Regression Estimator for Population Variance in Simple Random Sampling

Abstract

Accurate estimation of population variance plays a vital role in survey sampling, especially when simple random sampling is used. In this work, we propose a new generalized statistical inference in order to estimate the population variance using auxiliary information. We can use the relationship between the study variable and the auxiliary variable to construct a novel generalized class of estimators that is better performing in terms of minimum mean squared error (MSE) and has a higher percentage of relative efficiency than the traditional estimators. Theoretical properties of the proposed estimator such as the mean squared error, relative efficiency and bias are derived. The performance of the proposed generalized regression estimation estimator of the population variance under the simple random sampling design is assessed via simulation. The numerical findings reveal that the proposed estimator outperforms the competitors in all aspects. Also, the proposed estimator is robust as confirmed using various sample sizes and correlation coefficient. The research has made a significant contribution to the development of statistical procedures in survey sampling because the practical and efficient tools provided in the study were useful in estimating the variance.