The spatial sign covariance matrix and its application for robust correlation estimation

TL;DR

This paper explores the properties of the spatial sign covariance matrix, its eigenvalues, and introduces a robust, non-parametric correlation estimator for elliptical distributions, including a multivariate extension.

Contribution

It generalizes the spatial sign correlation coefficient to multivariate cases and analyzes its properties for robust correlation estimation.

Findings

Established the relationship between eigenvalues of the spatial sign covariance matrix and the shape matrix.

Developed a multivariate spatial sign correlation matrix.

Provided insights into the robustness of the estimator.

Abstract

We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case was used to construct the spatial sign correlation coefficient, which is a non-parametric and robust estimator for the correlation coefficient within the elliptical model. We consider a multivariate generalization, which we call the multivariate spatial sign correlation matrix.