The problem of zero-rate multiterminal hypothesis testing is revisited. A Neyman-Pearson-like test is proposed and its non-asymptotic performance is clarified; for short blocklength, it is numerically examined that the proposed test is superior to a previously known Hoeffding-like test proposed by Han-Kobayashi. For the large deviation regime, it is shown that our proposed test achieves the optimal trade-off between the type I and type II exponents shown 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 second-order 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.
['Shun Watanabe']
Neyman-Pearson Test for Zero-Rate Multiterminal Hypothesis Testing