On Weighted Multivariate Sign Functions

Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. These weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. We demonstrate methods of robust principal component analysis using weighted signs, and extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection.