  Work in the classification literature has shown that in computing a
classification function, one need not know the class membership of all
observations in the training set; the unlabeled observations still provide
information on the marginal distribution of the feature set, and can thus
contribute to increased classification accuracy for future observations. The
present paper will show that this scheme can also be used for the estimation of
class prior probabilities, which would be very useful in applications in which
it is difficult or expensive to determine class membership. Both parametric and
nonparametric estimators are developed. Asymptotic distributions of the
estimators are derived, and it is proven that the use of the unlabeled
observations does reduce asymptotic variance. This methodology is also extended
to the estimation of subclass probabilities.
