Improved estimation of population parameter of in the existence of nonresponse using auxiliary information

The issue of survey nonresponse causes substantial effects on the reliability, together with validity of study findings. This research develops precise estimation methods for two distinct nonresponse situations: when nonresponse happens to primary survey variables like the number of students, and when nonresponse includes survey variables together with the accompanying auxiliary variables. The proposed estimators receive full a performance assessment through derived equations for bias and mean square error (MSE) based on first-order approximation. The accuracy and reliability assessment depends heavily on MSE calculations, since this method effectively merges systematic error measurements with random error measurements. The MSE values of different estimators receive numerical evaluation through a comparative analysis under equivalent operational conditions for assessing proposed estimator performance outcomes. The research seeks to find the estimator with the minimal MSE because this selection results in the most trustworthy estimates under nonresponse conditions. All the findings from this study create important guidelines for building educational survey designs.