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On the Breakdown Properties of Some Multivariate M-Functionals*

On the Breakdown Properties of Some Multivariate M-Functionals*

Abstract. For probability distributions on ℝq, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler's [Ann. Statist. 15 (1987) 234] 'distribution-free' M-functional of scatter is given. These include a symmetrized version of Tyler's M-functional of scatter, and the multivariate t M-functionals of location and scatter. …