Incorporating the neutrosophic framework into kernel regression for predictive mean estimation.

In traditional statistics, all research endeavors revolve around utilizing precise, crisp data for the predictive estimation of population mean in survey sampling, when the supplementary information is accessible. However, these types of estimates often suffer from bias. The major aim is to uncover the most accurate estimates for the unknown value of the population mean while minimizing the mean square error (MSE). We have employed the neutrosophic approach, which is the extension of classical statistics that deals with the uncertain, vague, and indeterminate information, and proposed a neutrosophic predictive estimator of finite population mean using the kernel regression. The proposed estimator does not yield a single numerical value but instead provides an interval range within which the population parameter is likely to exist. This approach enhances the efficiency of the estimators by offering an estimated interval that encompasses the unknown value of the population mean with the least possible mean squared error (MSE). The simulation-based efficiency of the proposed estimator is discussed using the Sine, Bump and real-time temperature data set of Islamabad by using symmetric (Gaussian) kernel. The proposed non-parametric neutrosophic estimator has shown more effective results under the various bandwidth selectors than the adapted neutrosophic estimators.