Cerioli (2010) introduced a Mahalanobis distance-based
multivariate outlier detection methodology, the Iterated Reweighted
Minimum Covariance Determinant (IRMCD) method, that is more accurate,
both in the presence and absence of outliers, than previous approaches
using MCD-based Mahalanobis distances. The IRMCD method uses an approximation,
developed by Hardin and Rocke (2005), for the finite
sample distribution of MCD-based squared Mahalanobis distances. This
approximation, however, was developed for the maximum-breakdown point
case of the MCD estimate; its performance for MCD with other subsample
sizes has not been studied to our knowledge. Thus it is not clear that
one can rely on the IRMCD approach when using MCD with subsample sizes
other than the maximum-breakdown point case. These MCD variants are of
interest in applications (e.g., with financial data) where one is
hesitant to discard too much of
the data in building location and dispersion estimates. Hence, in this
technical note, we investigate how well Hardin and Rocke's approximation
works for the MCD in general. We use a simulation experiment more
extensive that the experiment performed by Hardin and Rocke to construct
a modified approximation for use with MCD-based squared Mahalanobis
distances. We conclude by validating the IRMCD method for some MCD variants
with larger subsample sizes that are of interest to financial practitioners.