Sign and rank covariance matrices

By Samuli Visuri, Hannu Oja. 2000

168 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/abc284603f37e4e8ee9370f960918c0e2e0bb39a

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In Applied Mathematics

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Outlier Detection for Compositional Data Using Robust Methods (2008, unknown): “A way out of this situation is to use covariance estimators which are less sensitive to deviations from elliptical symmetry, like estimators based on spatial signs or ranks (Visuri, Koivunen, and Oja, 2000).”
Multivariate Nonparametric Tests of Independence (2005, methodology): “(See Visuri, Oja, and Koivunen 2000 for the development of these rank covariance matrices.)”
ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions (2013, methodology): “sed on the multivariate Kendall's tau statistic, which is rst introduced in Choi and Marden (1998) for testing independence and is further used in estimating low-dimensional covariance matrices (Visuri et al., 2000; Oja, 2010) and principal components (Marden, 1999; Croux et al., 2002; Jackson ”
Invariant co‐ordinate selection (2009, background): “Other scatter statistics which lie within this class are the multivariate sign and rank scatter matrices; see for example Visuri et al (2000).”
Robust High-Dimensional Precision Matrix Estimation (2014, methodology): “To compare to a rowwise, but not cellwise robust estimator that can be computed in high dimensions, we consider the spatial sign covariance matrix [Visuri et al., 2000] Sinconssign (X) = 1 n n ∑ i=1 U(xi − µ̂)U(xi − µ̂)′, (25) where U(y) = ‖y‖−12 y if y 6= 0 and U(y) = 0 otherwise, and ‖y‖2 stands…”
Elliptical graphical modelling (2011, background): “One way to tackle this problem is to drop the affine equivariance and resort to robust “pairwise” estimators, such as the Gnanadesikan-Kettenring estimator (Gnanadesikan and Kettenring, 1972; Maronna and Zamar, 2002) or marginal sign and rank matrices (Visuri et al., 2000), see also Section 5.”
Sign and Rank Covariance Matrices: Statistical Properties and Application to Principal Components Analysis (2002, background): “Their most important properties are listed below. Full detail can be found in [9] and [ 10 ].”