Hypothesis testing with communication constraints

A new class of statistical problems is introduced, involving the presence of communication constraints on remotely collected data. Bivariate hypothesis testing, against , is considered when the statistician has direct access to data but can be informed about data only at a preseribed finite rate . For any fixed R the smallest achievable probability of an error of type with the probability of an error of type being at most is shown to go to zero with an exponential rate not depending on as the sample size goes to infinity. A single-letter formula for the exponent is given when (test against independence), and partial results are obtained for general . An application to a search problem of Chernoff is also given.