Csiszár's forward cutoff rate for testing between two arbitrary sources

Fady Alajaji*, Po-Ning Chen, Ziad Rached

*Corresponding author for this work

Research output: Contribution to journalConference article

1 Scopus citations

Abstract

The Csiszár forward β-cutoff rate (β < 0) for hypothesis testing is defined as the largest rate R0 ≥ 0 such that for all rates 0 < E < R0, 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 Dα(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 languageEnglish
Number of pages1
JournalIEEE International Symposium on Information Theory - Proceedings
DOIs
StatePublished - 12 Sep 2002
Event2002 IEEE International Symposium on Information Theory - Lausanne, Switzerland
Duration: 30 Jun 20025 Jul 2002

Fingerprint Dive into the research topics of 'Csiszár's forward cutoff rate for testing between two arbitrary sources'. Together they form a unique fingerprint.

  • Cite this