M-Functionals of Multivariate Scatter

Dümbgen, Lutz; Pauly, M.; Schweizer, Thomas (2015). M-Functionals of Multivariate Scatter. Statistics Surveys, 9, pp. 32-105. 10.1214/15-SS109

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This survey provides a self-contained account of M-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying M-functionals and discuss their weak continuity and differentiability. This is done in a rather general framework with matrix-valued random variables. By doing so we reveal a connection between Tyler's (1987) M-functional of scatter and the estimation of proportional covariance matrices. Moreover, this general framework allows us to treat a new class of scatter estimators, based on symmetrizations of arbitrary order. Finally these results are applied to M-estimation of multivariate location and scatter via multivariate t-distributions.

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 and Schweizer, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

1935-7516

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

27 Mar 2015 11:04

Last Modified:

26 Jun 2016 02:00

Publisher DOI:

10.1214/15-SS109

BORIS DOI:

10.7892/boris.65755

URI:

https://boris.unibe.ch/id/eprint/65755

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