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MA
2010
Springer

Asymptotic expansion of the minimum covariance determinant estimators

13 years 11 months ago
Asymptotic expansion of the minimum covariance determinant estimators
In Cator and Lopuha¨a [3] an asymptotic expansion for the MCD estimators is established in a very general framework. This expansion requires the existence and non-singularity of the derivative in a first-order Taylor expansion. In this paper, we prove the existence of this derivative for multivariate distributions that have a density and provide an explicit expression. Moreover, under suitable symmetry conditions on the density, we show that this derivative is non-singular. These symmetry conditions include the elliptically contoured multivariate location-scatter model, in which case we show that the minimum covariance determinant (MCD) estimators of multivariate location and covariance are asymptotically equivalent to a sum of independent identically distributed vector and matrix valued random elements, respectively. This provides a proof of asymptotic normality and a precise description of the limiting covariance structure for the MCD estimators.
Eric A. Cator, Hendrik P. Lopuhaä
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where MA
Authors Eric A. Cator, Hendrik P. Lopuhaä
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