(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this article, we used model base method (predictive approach) using auxiliary variables under simple random sampling. Based on the predictive approach the unobserved population along with the observed ones is considered. We found the results for bias, mean squared error both theoretically and numerically. The research analyzes sophisticated through predictive models because it successfully models complex non-linear research variable interactions combined with their auxiliary variables. The current work is evaluated through numerous applications which produce better improved estimation performances. The corresponding optimal strategies of the suggested estimators are explored together with their empirical and graphical analogues with various contemporary estimators of population mean. Some actual data sets are used in an empirical research. By means of a comparison between the mean square error of the proposed estimators with the mean square error of existing estimators under which the suggested class of estimator dominates the existing estimators. The favorable empirical results clearly demonstrate the superiority of the proposed estimators over the existing estimators.