On the Breakdown Properties of some Multivariate M-Functionals

Dümbgen, Lutz; Tyler, David E. (2005). On the Breakdown Properties of some Multivariate M-Functionals. Scandinavian journal of statistics, 32(2), pp. 247-264. Blackwell 10.1111/j.1467-9469.2005.00425.x

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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. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M-functional of scatter and of its symmetrized version are 1/q and inline image, respectively. For the multivariate t M-functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/(q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low-dimensional subspaces.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Dümbgen, Lutz

Subjects:

500 Science > 510 Mathematics

ISSN:

0303-6898

Publisher:

Blackwell

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

14 Dec 2015 10:45

Last Modified:

24 Jan 2017 17:07

Publisher DOI:

10.1111/j.1467-9469.2005.00425.x

BORIS DOI:

10.7892/boris.73749

URI:

https://boris.unibe.ch/id/eprint/73749

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