A new class of statistical problems is introduced, involving the presence of communication constraints on remotely collected data. Bivariate hypothesis testing, H0: PXY against [formula omitted], 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 e is shown to go to zero with an exponential rate not depending on e as the sample size goes to infinity. A single-letter formula for the exponent is given when [formula omitted] (test against independence), and partial results are obtained for general [formula omitted]. An application to a search problem of Chernoff is also given.
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences