Rank covariance matrix for a partially known covariance matrix

Abstract

Classical multivariate methods are often based on the sample covariance matrix, which is very sensitive to outlying observations. One alternative to the covariance matrix is the affine equivariant rank covariance matrix (RCM) that has been studied in Visuri et al. [2003. Affine equivariant multivariate rank methods.]. Statist. Plann. Inference 114, 161-185]. In this article we assume that the covariance matrix is partially known and study how to estimate the corresponding RCM. We use the properties that the RCM is affine equivariant and that the RCM is proportional to the inverse of the regular covariance matrix, and hence reduce the problem of estimating the original RCM to estimating marginal rank covariance matrices. This is a great computational advantage when the dimension of the original data vector is large. (C) 2008 Elsevier B.V. All rights reserved.

Keywords

multivariate ranks; rank covariance matrix; marginal rank covariance matrix; elliptical distributions; affine equivariance

Published in

Journal of Statistical Planning and Inference
2008, volume: 138, number: 12, pages: 3667-3673
Publisher: Elsevier

SLU Authors

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

• DOI: https://doi.org/10.1016/j.jspi.2007.11.015

Permanent link to this page (URI)

https://res.slu.se/id/publ/19300