  So-called "classification trimmed likelihood curves" have been proposed as a
useful heuristic tool to determine the number of clusters and trimming
proportion in trimming-based robust clustering methods. However, these curves
needs a careful visual inspection, and this way of choosing parameters requires
subjective decisions. This work is intended to provide theoretical background
for the understanding of these curves and the elements involved in their
derivation. Moreover, a parametric bootstrap approach is presented in order to
automatize the choice of parameter more by providing a reduced list of
"sensible" choices for the parameters. The user can then pick a solution that
fits their aims from that reduced list.
