On weighted multivariate sign functions
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Date
2022-05-21
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Citation of Original Publication
Majumdar, 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.
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Attribution-NonCommercial-NoDerivatives 4.0 International CC BY-NC-ND 4.0 Deed
Abstract
Multivariate 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.