On enhanced estimation and monitoring of population variance using robust auxiliary parameters based estimators

Abstract

Summary Searching for efficient estimators of population variance as compared to sample variance has been the key area of interest of the researchers. Auxiliary variable has helped very much in finding estimators more efficient than sample variance. Auxiliary variable is greatly correlated with main study variable. Many authors including Isaki (J Am Stat Assoc 1983, 78, 117) used positively correlated auxiliary variable in the form of various conventional and non‐conventional auxiliary parameters and suggested different ratio type estimators of population variance. In this article, we have suggested a naïve class of variance estimators based on some robust auxiliary parameters, which deals with the outliers in the data. The properties including bias and Mean Square Error (MSE) of suggested family of estimators are studied up to first order of approximation. The theoretical as well as empirical comparison of introduced family of estimators is carried out with competing variance estimators. The estimator with the least MSE is recommended in different areas of applications. At last, the Shewhart type control charts based on the proposed estimators are also studies for application in quality control.