Leveraging Rank Information for Robust Regression Analysis: A Nomination Sampling Approach

This paper introduces a novel methodology for robust regression analysis when traditional mean regression falls short due to the presence of outliers. Unlike conventional approaches that rely on simple random sampling (SRS), our methodology leverages median nomination sampling (MedNS) by utilizing readily available ranking information to obtain training data that more accurately captures the central tendency of the underlying population, thereby enhancing the representativeness of the sample in the presence of extensive outliers in the population. We propose a new loss function that integrates the extra rank information of MedNS data during the training phase of model fitting, thus offering a form of robust regression. Further, we provide an alternative approach that translates the median regression estimation using MedNS to corresponding problems under SRS. Through simulation studies, including a high-dimensional and a nonlinear regression setting, we evaluate the efficacy of our proposed approach compared to its SRS counterpart by comparing the integrated mean squared error of regression estimates. We observe that our proposed method provides higher relative efficiency (RE) compared to its SRS counterparts. Lastly, the proposed methods are applied to a real data set collected for body fat analysis in adults.