  The problem of zero-rate multiterminal hypothesis testing is revisited from
the perspective of information-spectrum approach and finite blocklength
analysis. A Neyman-Pearson-like test is proposed and its non-asymptotic
performance is clarified; for a short block length, it is numerically
determined that the proposed test is superior to the previously reported
Hoeffding-like test proposed by Han-Kobayashi. For a large deviation regime, it
is shown that our proposed test achieves an optimal trade-off between the type
I and type II exponents presented by Han-Kobayashi. Among the class of
symmetric (type based) testing schemes, when the type I error probability is
non-vanishing, the proposed test is optimal up to the second-order term of the
type II error exponent; the latter term is characterized in terms of the
variance of the projected relative entropy density. The information geometry
method plays an important role in the analysis as well as the construction of
the test.
