Asymptotic expansion of the minimum covariance determinant estimators

@article{Cator2010AsymptoticEO,
  title={Asymptotic expansion of the minimum covariance determinant estimators},
  author={Eric A. Cator and Hendrik P. Lopuha{\"a}},
  journal={J. Multivariate Analysis},
  year={2010},
  volume={101},
  pages={2372-2388}
}
In Cator and Lopuhaä [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… CONTINUE READING

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