  We consider Bayesian multiple statistical classification problem in the case
where the unknown source distributions are estimated from the labeled training
sequences, then the estimates are used as nominal distributions in a robust
hypothesis test. Specifically, we employ the DGL test due to Devroye et al. and
provide non-asymptotic, exponential upper bounds on the error probability of
classification. The proposed upper bounds are simple to evaluate and reveal the
effects of the length of the training sequences, the alphabet size and the
numbers of hypothesis on the error exponent. The proposed method can also be
used for large alphabet sources when the alphabet grows sub-quadratically in
the length of the test sequence. The simulations indicate that the performance
of the proposed method gets close to that of optimal hypothesis testing as the
length of the training sequences increases.
