The spatial sign covariance matrix with unknown location

TL;DR

This paper investigates the properties of the spatial sign covariance matrix when the location parameter is unknown, demonstrating its consistency and asymptotic normality, with simulations comparing mean and median estimators.

Contribution

It establishes the theoretical properties of the spatial sign covariance matrix with unknown location and compares different estimators through simulations.

Findings

The spatial sign covariance matrix is consistent and asymptotically normal.

Different asymptotic behaviors are observed when using mean versus median as location estimators.

Simulations illustrate the theoretical results and differences between estimators.

Abstract

The consistency and asymptotic normality of the spatial sign covariance matrix with unknown location are shown. Simulations illustrate the different asymptotic behavior when using the mean and the spatial median as location estimator.