TY - JOUR

T1 - Csiszár's forward cutoff rate for testing between two arbitrary sources

AU - Alajaji, Fady

AU - Chen, Po-Ning

AU - Rached, Ziad

PY - 2002/6/30

Y1 - 2002/6/30

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0036350719&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2002.1023487

DO - 10.1109/ISIT.2002.1023487

M3 - Conference article

AN - SCOPUS:0036350719

SN - 2157-8095

SP - 215

EP - 215

JO - IEEE International Symposium on Information Theory - Proceedings

JF - IEEE International Symposium on Information Theory - Proceedings

M1 - 1023487

T2 - 2002 IEEE International Symposium on Information Theory

Y2 - 30 June 2002 through 5 July 2002

ER -