OGK Approach for Accurate Mean Estimation in the Presence of Outliers

This paper proposes a new family of robust estimators of means, depending on the Orthogonalized Gnanadesikan–Kettenring (OGK) covariance matrix. These estimators are computationally feasible and robust replacements of the Minimum Covariance Determinant (MCD) estimator in survey sampling contexts involving auxiliary information. With the growing popularity of outliers in environmental data, as in the case of measuring solar radiation, conventional estimators like the sample mean or the Ordinary Least Squares (OLS) regression-based estimators are both biased and unreliable. The suggested OGK-based exponential-type estimators combine robust measures of location and dispersion and have a considerable advantage in the estimation of the population mean when auxiliary variables such as temperature are highly correlated with the variable of interest. The MSE property of OGK-based estimators is also obtained through a detailed theoretical derivation with the expressions of optimal weights. Performance was further proved using real-world and simulated data on solar radiation, as well as by demonstrating lower MSEs and higher PREs in comparison to MCD-based estimators. These results show that OGK-based estimators are highly efficient and robust in actual and artificially contaminated situations and hence are a good option in robust survey sampling and environmental data analysis.