Under classical statistics, research typically relies on precise data to estimate the population mean when auxiliary information is available. Outliers can pose a significant challenge in this process. The ultimate goal is to determine the most accurate estimates of the population mean while minimizing variance. Neutrosophic statistics is a generalization of classical statistics that deals with imprecise, uncertain data. Our research introduces the neutrosophic Hartley–Ross-type ratio estimators for estimating the population mean of neutrosophic data, even in the presence of outliers. We also incorporate neutrosophic versions of several robust regression methods, including LAD, Huber-M, Hampel-M, and Tukey-M. Our approach assumes that the study variable is both non-sensitive and sensitive, meaning that it can cause discomfort to participants during personal interviews, and measurement errors can occur due to dishonest responses. To address potential measurement errors, we propose the use of neutrosophic scrambling response models. Our proposed neutrosophic robust estimators are more effective than existing classical estimators, as confirmed by a computer-based numerical study using real data and simulation.
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