Central limit theorem and influence function for the MCD estimators at general multivariate distributions

By Eric A. Cator, Hendrik P. Lopuhaä. 2009

56 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/57723e6fc4571a4de1fc41db63d59e546000a0a8

Citations in the corpus

• Outlyingness weighted covariation (2011, unknown): “For multivariate normal data, the MCD covariance estimate has been shown to be consistent and asymptotically normal by Butler et al. (1993) and Cator and Lopuhaä (2011).”