  The two main topics of this paper are the introduction of the "optimally
tuned improper maximum likelihood estimator" (OTRIMLE) for robust clustering
based on the multivariate Gaussian model for clusters, and a comprehensive
simulation study comparing the OTRIMLE to Maximum Likelihood in Gaussian
mixtures with and without noise component, mixtures of t-distributions, and the
TCLUST approach for trimmed clustering. The OTRIMLE uses an improper constant
density for modelling outliers and noise. This can be chosen optimally so that
the non-noise part of the data looks as close to a Gaussian mixture as
possible. Some deviation from Gaussianity can be traded in for lowering the
estimated noise proportion. Covariance matrix constraints and computation of
the OTRIMLE are also treated. In the simulation study, all methods are
confronted with setups in which their model assumptions are not exactly
fulfilled, and in order to evaluate the experiments in a standardized way by
misclassification rates, a new model-based definition of "true clusters" is
introduced that deviates from the usual identification of mixture components
with clusters. In the study, every method turns out to be superior for one or
more setups, but the OTRIMLE achieves the most satisfactory overall
performance. The methods are also applied to two real datasets, one without and
one with known "true" clusters.
