Symmetrised M-estimators of multivariate scatter

Seija Sirkiä, Sara Taskinen and Hannu Oja

Journal of Multivariate Analysis, 2007, vol. 98, issue 8, 1611-1629

Abstract: In this paper we introduce a family of symmetrised M-estimators of multivariate scatter. These are defined to be M-estimators only computed on pairwise differences of the observed multivariate data. Symmetrised Huber's M-estimator and Dümbgen's estimator serve as our examples. The influence functions of the symmetrised M-functionals are derived and the limiting distributions of the estimators are discussed in the multivariate elliptical case to consider the robustness and efficiency properties of estimators. The symmetrised M-estimators have the important independence property; they can therefore be used to find the independent components in the independent component analysis (ICA).

Keywords: Efficiency; Elliptical; distribution; Influence; function; M-estimator; Robustness; Scatter; matrix (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (8)

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