Mixed-optimum Estimators for Estimating Finite Population Mean in the Presence of Outliers Using Auxiliary Variable under Simple Random Sampling

In sample survey the nature of correlation between the study and auxiliary variables plays a crucial role in improving the accuracy of the estimates. In this study a generalized mixed-optimum estimators that handle the three nature of correlation for different values (-1,0,1) of the scalar was proposed for estimating the finite population mean when there is information on the minimum and maximum values of the auxiliary variable and when both the auxiliary and study variables exhibit extreme values. The expression for the mean squared errors and biases were derived to the first order of approximation. The performance of the proposed estimators, relative to conventional methods, has been rigorously analyzed, revealing notable improvements. Theoretical analysis confirmed that correcting the estimators for mitigating maximum and minimum values enhanced its efficiency, and these findings have been empirically validated through comprehensive numerical analysis.