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

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3 Author(s)
Alajaji, F. ; Dept. of Math. & Stat., Queen''s Univ., Kingston, Ont., Canada ; Po-Ning Chen ; Rached, Z.

The Csisza forward β-cutoff rate (β<0) for hypothesis testing is defined as the largest rate R0≥0 such that for all rates 00, 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 Csiszar (see IEEE Transactions on Information Theory, vol.41, p.26-34, January 1995) that the forward β-cutoff rate for testing between a hypothesis X against an alternative hypothesis X~ based on independent and identically distributed samples, is given by Renyi's α-divergence Dα(X||X~), 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).

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Information Theory, 2002. Proceedings. 2002 IEEE International Symposium on

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