Rank Covariance Matrix for a Partially Known Covariance Matrix

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.