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Title: On the computation of symmetrized M-estimators of scatter Authors:  Jari Miettinen - University of Jyvaskyla (Finland) [presenting]
Klaus Nordhausen - University of Jyvaskyla (Finland)
Sara Taskinen - University of Jyvaskyla (Finland)
David Tyler - Rutgers (United States)
Abstract: The symmetrized version of a multivariate scatter functional is obtained when the functional is applied to the pairwise differences of the observations. Sometimes the symmetrization increases the efficiency, but perhaps the most important benefit is that the symmetrized scatter matrices always have the independence property, that is, they are diagonal when the components are mutually independent. A scatter matrix needs the independence property when it is used as a robust substitute of the sample covariance matrix in certain multivariate methods, as for example in independent component analysis and graphical modeling. The obvious disadvantage of symmetrization is the number of pairwise differences which grows very fast with the number of observations. The computational aspects of symmetrized M-estimates are considered. The computation time of the standard fixed point algorithm is compared to those of incomplete, parallel, and partial Newton algorithms. Also the efficiency loss of the incomplete estimator, which uses only a subset of the pairwise differences, is studied.