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) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Dümbgen, Lutz, Schweizer, Thomas |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1935-7516 |
Language: |
English |
Submitter: |
Lutz Dümbgen |
Date Deposited: |
27 Mar 2015 11:04 |
Last Modified: |
05 Dec 2022 14:44 |
Publisher DOI: |
10.1214/15-SS109 |
BORIS DOI: |
10.7892/boris.65755 |
URI: |
https://boris.unibe.ch/id/eprint/65755 |
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