Rank covariance matrix estimation of a partially known covariance matrix |
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Authors: | Kristi Kuljus Dietrich von Rosen |
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Affiliation: | 1. Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden;2. Department of Biometry and Engineering, Swedish University of Agricultural Sciences, P.O. Box 7032, 750 07 Uppsala, Sweden |
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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. J. 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. |
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Keywords: | Multivariate ranks Rank covariance matrix Marginal rank covariance matrix Elliptical distributions Affine equivariance |
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