  We propose a universal classifier for binary Neyman-Pearson classification
where null distribution is known while only a training sequence is available
for the alternative distribution. The proposed classifier interpolates between
Hoeffding's classifier and the likelihood ratio test and attains the same error
probability prefactor as the likelihood ratio test, i.e., the same prefactor as
if both distributions were known. In addition, like Hoeffding's universal
hypothesis test, the proposed classifier is shown to attain the optimal error
exponent tradeoff attained by the likelihood ratio test whenever the ratio of
training to observation samples exceeds a certain value. We propose a lower
bound and an upper bound to the training to observation ratio. In addition, we
propose a sequential classifier that attains the optimal error exponent
tradeoff.
