Majumdar, SubhabrataChatterjee, Snigdhansu2025-03-112025-03-112022-05-21Majumdar, Subhabrata, and Snigdhansu Chatterjee. “On Weighted Multivariate Sign Functions.” Journal of Multivariate Analysis 191 (September 1, 2022): 105013. https://doi.org/10.1016/j.jmva.2022.105013.https://doi.org/10.1016/j.jmva.2022.105013http://hdl.handle.net/11603/37802Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.19 pagesen-USAttribution-NonCommercial-NoDerivatives 4.0 International CC BY-NC-ND 4.0 Deedhttps://creativecommons.org/licenses/by-nc-nd/4.0/Sufficient dimension reductionOutlier detectionPrincipal component analysisData depthMultivariate signText