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}againstH_{1}: P_{={XY}}, is considered when the statistician has direct access toYdata but can be informed aboutXdata only at a preseribed finite rateR. For any fixed R the smallest achievable probability of an error of type2with the probability of an error of type1being at mostepsilonis shown to go to zero with an exponential rate not depending onepsilonas the sample size goes to infinity. A single-letter formula for the exponent is given whenP_{={XY}} = P_{X} times P_{Y}(test against independence), and partial results are obtained for generalP_{={XY}}. An application to a search problem of Chernoff is also given.
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