Abstract
A new class of statistical problems is introduced, involving the presence of communication constraints on remotely collected data. Bivariate hypothesis testing, \(H_0: P_{XY}\) against \(H_1: P_{\bar{XY}}\), is considered when the statistician has direct access to Y data but can be informed about X data only at a prescribed finite rate R. For any fixed R the smallest achievable probability of an error of type 2 with the probability of an error of type 1 being at most \(\epsilon \) is shown to go to zero with an exponential rate not depending on \(\epsilon \) as the sample size goes to infinity.
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