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 a??ne equivariant rank covariance matrix (RCM) that has been studied for example in Visuri et al. (2003). 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 a??ne equivariant and that the RCM is proportional to the inverse of the regular covariance matrix, and reduce the problem of estimating the RCM to estimating marginal rank covariance matrices. This is a great advantage when the dimension of the original data vectors is large

Keywords

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

Published in

Research report (Centre of Biostochastics)
2006, number: 1, pages: 1-19
Publisher: Cnetre of Biostochastics, SLU

SLU Authors

• Kuljus, Kristi

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

• von Rosen, Dietrich

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

Permanent link to this page (URI)

https://res.slu.se/id/publ/9021