Dümbgen, Lutz
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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.
| Document 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 > Institut für Mathematik |
| DDC-classification: | 310 General statistics 510 Mathematics |
| Uncontrolled Keywords: | Differentiability; dimensional asymptotics; elliptical symmetry; M-functional; scatter matrix; symmetrization |
| Series: | 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. |
