Symmetrised M-estimators of multivariate scatter
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).
Volume (Year): 98 (2007)
Issue (Month): 8 (September)
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References listed on IDEAS
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- Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
- Lutz Dümbgen & David E. Tyler, 2005. "On the Breakdown Properties of Some Multivariate M-Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 247-264.
- Hossjer, O. & Croux, C. & Rousseeuw, P. J., 1994. "Asymptotics of Generalized S-Estimators," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 148-177, October.
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