Neutrosophic Mean Estimators Using Extreme Indeterminate Observations in Sample Surveys

Abstract

 In classical statistics, research typically relies on precise data to estimate the population mean,
 especially when auxiliary information is available. However, in the presence of outliers, conventional statistical
 approaches that depend on accurate data and auxiliary information encounter challenges. The primary objective
 is to attain the most accurate population mean estimates while minimizing the mean square error. Neutrosophic
 statistics, a more attractive framework than classical statistics, deals with data characterized by imprecision and
 uncertainty. In this current article, we adapt S¨ arndal’s strategy and introduce neutrosophic mean estimators,
 applying them to meteorological data, specifically stratified dew point data. In these proposed estimators, the
 incorporation of auxiliary information and the application of robust techniques address issues that arise due to
 outliers and imprecise observations. These factors can otherwise undermine the effectiveness of neutrosophic
 estimation methods. The article also suggests combining auxiliary information with extremely indeterminate
 neutrosophic observations, utilizing robust regression methods (Huber-M, Hampel-M, and Tukey-M), as well as
 the quantile regression technique. These approaches enhance the neutrosophic mean estimation process. The
 outcomes, which include the utilization of dew point data, showcase the superior performance of the proposed
 estimators compared to adapted estimators in a neutrosophic context. Ultimately, this study provides valuable
 insights by taking an initial step in defining and utilizing the concept of neutrosophic indeterminate extreme
 observations

DOI: 10.5281/zenodo.14707260