### Abstract

The Csiszár forward β-cutoff rate (β < 0) for hypothesis testing is defined as the largest rate R_{0} ≥ 0 such that for all rates 0 < E < R_{0}, the smallest probability of type 1 error of sample size-n tests with probability of type 2 error ≤ e^{-nE} is asymptotically vanishing as e^{-nβ(E-R0)}. It was shown by Csiszár that the forward β-cutoff rate for testing between a null hypothesis X̄ against an alternative hypothesis X based on independent and identically distributed samples, is given by Rényi's α-divergence D_{α}(X∥X̄), where α = 1/(1 - β). In this work, we show that the forward β-cutoff rate for the general hypothesis testing problem is given by the lim inf α-divergence rate. The result holds for an arbitrary abstract alphabet (not necessarily countable).

Original language | English |
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Number of pages | 1 |

Journal | IEEE International Symposium on Information Theory - Proceedings |

DOIs | |

State | Published - 12 Sep 2002 |

Event | 2002 IEEE International Symposium on Information Theory - Lausanne, Switzerland Duration: 30 Jun 2002 → 5 Jul 2002 |