Hypothesis testing with multiterminal data compression

The multiterminal hypothesis testingH: XYagainstH̄: X̄Ȳis considered whereXⁿ (X̄ⁿ)andYⁿ (Ȳⁿ)are separately encoded at ratesR₁andR₂, respectively. The problem is to determine the minimumβₙof the second kind of error probability, under the condition that the first kind of error probabilityαₙ ≤ a prescribed0 < ε < 1. A good lower boundθL(R₁, R₂)on the power exponentθ (R₁, R₂,ε)= lim infn → ∞(-1/n log βₙ)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 withR₂ = to full side information forYⁿ(Ȳⁿ). In particular, the compact solution is established to the complete data compression cases, which are useful in statistics from the practical point of view.