  Consider a distributed detection problem in which the underlying
distributions of the observations are unknown; instead of these distributions,
noisy versions of empirically observed statistics are available to the fusion
center. These empirically observed statistics, together with source (test)
sequences, are transmitted through different channels to the fusion center. The
fusion center decides which distribution the source sequence is sampled from
based on these data. For the binary case, we derive the optimal type-II error
exponent given that the type-I error decays exponentially fast. The type-II
error exponent is maximized over the proportions of channels for both source
and training sequences. We conclude that as the ratio of the lengths of
training to test sequences $\alpha$ tends to infinity, using only one channel
is optimal. By calculating the derived exponents numerically, we conjecture
that the same is true when $\alpha$ is finite. We relate our results to the
classical distributed detection problem studied by Tsitsiklis, in which the
underlying distributions are known. Finally, our results are extended to the
case of $m$-ary distributed detection with a rejection option.
