Cryo electron microscopy is a measurement modality which provides
images from which 3-D reconstructions of biological particles such
as viruses can be estimated. When the specimen is composed of mixtures
of particles of different types, the 3-D reconstruction problem must
be solved jointly with a pattern classification problem. The performance
of the estimators is not well understood because the computations are
not suitable for analytical results and are too large for extensive
Monte Carlo results. The problem formulation typically has nuisance
parameters and different treatments of the nuisance parameters lead
to different estimators. In this paper two types of estimators and
two model problems are studied with the conclusion that it is difficult
to improve upon maximum likelihood estimators based on integrating out
the nuisance parameters.