Robust detection of signed outliers in multivariate data with applications to early identification of risk for autism.

Abstract

This article proposes an approach for detecting multivariate outliers that combines robust estimation methods with signed detection information. Our method uses the Mahalanobis distance to quantify each observation's extremeness from the expected value relative to the covariance matrix, and we leverage robust estimation tools, i.e., the minimum covariance determinant, to estimate the mean vector and covariance matrix used in the Mahalanobis distance calculation. Furthermore, we incorporate a signing element into the distance calculation to give researchers greater control over the specific regions of multivariate space that should be prioritized when searching for outliers, which allows for more targeted risk assessment and classification. Lastly, we unify the robust and signed elements into a framework that can be used within bilinear models such as principal components analysis and factor analysis. Using simulated and real data examples, we demonstrate that the proposed approach can result in improved risk assessment and outlier detection, particularly when the sample is contaminated with a moderate-to-large number of outliers that have noteworthy contamination strengths. Overall, our results show that making use of a robust method when assessing multivariate risk leads to more accurate estimates, particularly when combined with relevant signing information. (PsycInfo Database Record (c) 2025 APA, all rights reserved).