In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source distributions are not known, however one has access to labeled training sequences, of length N, from each source. We consider the case where the unknown source distributions are estimated from the training sequences, then the estimates are used as nominal distributions in a robust hypothesis test. Specifically, we consider the robust DGL test due to Devroye et al. and provide non-asymptotic exponential bounds, that are functions of N{n, on the error probability of classification.