Neutrosophic Statistics with Outliers Data: Utilizing Neutrosophic Median Absolute Deviation to Estimate the Mean Parameter Using Neutrosophic Modified One Step M-Estimator

Classical statistical methods rely on precise data to estimate population means using auxiliary information but often face issues like bias and high mean squared error (MSE). Neutrosophic statistics extend classical approaches by incorporating vague, indeterminate, and uncertain data. This study introduces the Modified One-Step M-estimator (NMOM), which utilizes auxiliary information to improve estimation accuracy. The Neutrosophic Median Absolute Deviation (NMAD) is also employed to measure robustness against outliers and uncertainty. Empirical studies and simulations compare NMOM with the Neutrosophic Standard Mean (NSM) using metrics such as mean, median, standard deviation, covariance, NMAD, number of outliers, and NMSE. Results show that NMOM is more robust than NSM, particularly in managing outliers, reducing variance, and achieving lower MSE. The use of NMAD strengthens NMOM’s ability to produce reliable estimates under uncertain data conditions. This highlights NMOM’s effectiveness in fields like finance, engineering, and medicine, where data imprecision is a key concern.