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.
Bibliographical noteFunding Information:
We thank the Editor, Associate Editor, and two anonymous referees for their insightful comments that led to improvements in the paper. The research of SC is partially supported by the US National Science Foundation grants 1737918 , 1939916 and 1939956 and a grant from Cisco Systems Inc.
© 2022 Elsevier Inc.
- Data depth
- Multivariate sign
- Outlier detection
- Principal component analysis
- Sufficient dimension reduction