title: The Asymptotic Behavior of Tyler's M-Estimator of Scatter in High Dimension
creator: Dümbgen, Lutz
subject: 310
subject: 310 General statistics
subject: 510
subject: 510 Mathematics
description: It is shown that Tyler's (1987) M-functional of scatter, whichis a robust surrogate for the covariance matrix of a distribution on R^p ,is Fr'echet-differentiable with respect to the weak topology. This propertyis derived in an asymptotic framework, where the dimension p may tend toinfinity. If applied to the empirical distribution of n i.i.d. randomvectors with elliptically symmetric distribution, the resulting estimatorhas the same asymptotic behavior as the sample covariance matrix in anormal model, provided that p tends to infinity and p/n tends to zero.
date: 1997-05
type: Working paper
type: info:eu-repo/semantics/workingPaper
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/20935/1/beitrag.23.pdf
identifier: DOI:10.11588/heidok.00020935
identifier: urn:nbn:de:bsz:16-heidok-209354
identifier:   Dümbgen, Lutz  (1997) The Asymptotic Behavior of Tyler's M-Estimator of Scatter in High Dimension.  [Working paper]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/20935/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng