An Improved and Robust Class of Variance Estimator

Document Type: Article

Authors

1 Department of Statistics, Government College University, Faisalabad, 38000, Pakistan

2 College of Statistical and Actuarial Sciences University of the Punjab Lahore, Pakistan

3 Department of Statistics, University of Sargodha, Sargodha, Pakistan

4 Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

Abstract

The ratio, product, and regression estimators are commonly constructed based on the conventional measures such as mean, median, quartiles, semi-interquartile range, semi-interquartile average, coefficient of skewness, and coefficient of kurtosis. In case of the presence of outliers, these conventional measures lose their efficiency/performance ability and hence are of less efficient as compared to those measures which performed efficiently in the presence of outliers. This study offers improved class of estimators for estimating the population variance using robust dispersion measures such as probability-weighted moments, Gini’s, Downton’s and Bickel and Lehmann measures of an auxiliary variable. Bias, Mean square error (MSE) and minimum MSE 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 an environment protection data. The results reveal that the proposed estimators perform better than its competitors and are robust, not only in simple conditions but also in the presence of outliers.

Keywords