### 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 [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.

Original language | English |
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Pages (from-to) | 533-542 |

Number of pages | 10 |

Journal | IEEE Transactions on Information Theory |

Volume | 32 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jul 1986 |

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*32*(4), 533-542. https://doi.org/10.1109/TIT.1986.1057194