  A number of results related to statistical classification on convex sets are
presented. In particular, the focus is on the case where some of the covariates
in the data and observation being classified can be missing. The form of the
optimal classifier is derived when the class-conditional densities are uniform
over convex regions. In practice, the underlying convex sets are often unknown
and must be estimated with a set of data. In this case, the convex hull of a
set of points is shown to be a consistent estimator of the underlying convex
set. The problem of estimation is further complicated since the number of
points in each convex hull is itself a random variable. The corresponding
plug-in version of the optimal classifier is derived and shown to be Bayes
consistent.
