Hypothesis testing with multiterminal data compression

The multiterminal hypothesis testingH: XYagainstH?: X?Y?is considered whereX^{n} (X?^{n})andY^{n} (Y?^{n})are separately encoded at ratesR_{1}andR_{2}, respectively. The problem is to determine the minimumbeta_{n}of the second kind of error probability, under the condition that the first kind of error probabilityalpha_{n} leq epsilonfor a prescribed0 < epsilon < 1. A good lower boundtheta_{L}(R_{1}, R_{2})on the power exponenttheta (R_{1}, R_{2},epsilon)= lim inf_{n rightarrow infty}(-1/n log beta_{n})is given and several interesting properties are revealed. The lower bound is tighter than that of Ahlswede and Csiszár. Furthermore, in the special case of testing against independence, this bound turns out to coincide with that given by them. The main arguments are devoted to the special case withR_{2} = inftycorresponding to full side information forY^{n}(Y?^{n}). In particular, the compact solution is established to the complete data compression cases, which are useful in statistics from the practical point of view.