# On Weighted Multivariate Sign Functions

## TL;DR

This paper introduces data-dependent weights to multivariate sign functions, enhancing robustness and efficiency in estimation and inference, with applications in location estimation, PCA, dimension reduction, and outlier detection.

## Contribution

It proposes a novel weighted sign function approach that improves robustness and efficiency over traditional methods in multivariate analysis.

## Key findings

- Weighted signs retain robustness properties.
- Significant efficiency improvements demonstrated.
- Effective in various multivariate applications.

## 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.