TY  - GEN
N1  - 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.
N2  - 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.
KW  - Differentiability; dimensional asymptotics; elliptical symmetry; M-functional; scatter matrix; symmetrization
AV  - public
Y1  - 1997/05//
TI  - The Asymptotic Behavior of Tyler's M-Estimator of Scatter in High Dimension
ID  - heidok20935
CY  - Heidelberg
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/20935/
A1  - Dümbgen, Lutz
EP  - 38
ER  -