Central limit theorem and influence function for the MCD estimators at general multivariate distributions
Statistics Theory
2012-05-10 v3 Statistics Theory
Abstract
We define the minimum covariance determinant functionals for multivariate location and scatter through trimming functions and establish their existence at any multivariate distribution. We provide a precise characterization including a separating ellipsoid property and prove that the functionals are continuous. Moreover, we establish asymptotic normality for both the location and covariance estimator and derive the influence function. These results are obtained in a very general multivariate setting.
Cite
@article{arxiv.0907.0079,
title = {Central limit theorem and influence function for the MCD estimators at general multivariate distributions},
author = {Eric A. Cator and Hendrik P. Lopuhaä},
journal= {arXiv preprint arXiv:0907.0079},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.3150/11-BEJ353 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)