An improved and robust class of variance estimator

The ratio, product, and regression estimators are commonly constructed based on conventional measures such as mean, median, quartiles, semi-interquartile range, semi-interquartile average, coefficient of skewness, and coefficient of kurtosis. In the case of the presence of outliers, these conventional measures lose their efficiency/performance ability and hence are less efficient as compared to those measures which performed efficiently in the presence of outliers. This study offers an improved class of estimators for estimating the population variance using robust dispersion measures such as probability-weighted moments, Gini, Downton and Bickel, and Lehmann measures of an auxiliary variable. Bias, mean square error and minimum mean square error of the suggested class of estimators have been derived. Application with two natural data sets is also provided to explain the proposal for practical considerations. In addition, a robustness study is also carried out to evaluate the performance of the proposed estimators in the presence of outliers by using environmental protection data. The results reveal that the proposed estimators perform better than their competitors and are robust, not only in simple conditions but also in the presence of outliers.