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. 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.Comment: Keywords: Multivariate sign, Principal component analysis, Data depth, Sufficient dimension reductio

Spatial Sign Correlation

A new robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied and compared to other robust correlation estimators by means of numerical simulations.Comment: 20 pages, 7 figures, 2 table

Robust estimation in simultaneous equations models

In this paper we review existing work on robust estimation for simultaneous equations models. Then we discuss three strategies for obtaining estimators with a high breakdown point, a controllable efficiency, and a reasonable computational cost: (a) robustifying Three-Stages Least Squares, (b) robustifying the Full Information Maximum Likelihood method by minimizing the determinant of a robust covariance matrix of residuals, and (c) generalizing multivariate tauestimators (Lopuhaa 1991) to these models. The latter seems the most promising approach