Ridge regression-based mean estimators using bivariate auxiliary information

The regression coefficient is commonly employed in regression-type mean estimators. However, outliers and co-linearity are two main challenges in regression analysis. The existence of such issues may produce extremely poor estimates or may be conducive to wrong information regarding the coefficients of regression. As a result, several corrective strategies have been proposed to treat these issues. One of these strategies is robust regression which is less affected by outliers, and ridge regression, which is used to address co-linearity. As shown in the survey sampling, the utilization of auxiliary information and non-traditional measures of location outperformed current conventional estimators, particularly in the presence of outliers. To handle these two problems (outliers and co-linearity) at the same time, ridge regression estimators are employed to propose a new family of estimators to estimate the population mean using bivariate auxiliary information. The general forms of minimum mean squared error are also derived. In terms of the percentage relative efficiency related to the various numerical illustrations based on real-life data sets and simulation studies, the proposed estimators have more efficient performance than the considered competitive estimators in the presence and absence of outliers.