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The Asymptotic Behavior of Tyler's M-Estimator of Scatter in High Dimension

Dümbgen, Lutz

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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.

Item Type: Working paper
Place of Publication: Heidelberg
Edition: revised May 1997
Date Deposited: 13 Jun 2016 09:18
Date: May 1997
Number of Pages: 38
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 310 General statistics
510 Mathematics
Uncontrolled Keywords: Differentiability; dimensional asymptotics; elliptical symmetry; M-functional; scatter matrix; symmetrization
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: 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.
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