eprintid: 20935
rev_number: 15
eprint_status: archive
userid: 2326
dir: disk0/00/02/09/35
datestamp: 2016-06-13 09:18:57
lastmod: 2016-06-24 08:00:07
status_changed: 2016-06-13 09:18:57
type: workingPaper
metadata_visibility: show
creators_name: Dümbgen, Lutz
title: The Asymptotic Behavior of Tyler's M-Estimator of Scatter in High Dimension
subjects: ddc-310
subjects: ddc-510
divisions: i-110400
keywords: Differentiability; dimensional asymptotics; elliptical symmetry; M-functional; scatter matrix; symmetrization
note: This is an extended version of the paper "On Tyler's M-functional of scatter in
high dimension" which has been tentatively accepted for publication in the Annals of the
Institute of Statistical Mathematics (50 (1998), pp. 471-491). 
The present version contains some additional results and more detailed proofs.
abstract: 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
id_scheme: DOI
id_number: 10.11588/heidok.00020935
schriftenreihe_cluster_id: sr-10a
schriftenreihe_order: 23
ppn_swb: 1657176029
own_urn: urn:nbn:de:bsz:16-heidok-209354
language: eng
bibsort: DUMBGENLUTTHEASYMPTO199705
full_text_status: public
place_of_pub: Heidelberg
pages: 38
edition: revised May 1997
citation:   Dümbgen, Lutz  (1997) The Asymptotic Behavior of Tyler's M-Estimator of Scatter in High Dimension.  [Working paper]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/20935/1/beitrag.23.pdf