A Spectral Representation Of The Simple Hypothesis Testing Problem
2026 IEEE International Symposium on Information Theory, ISIT 2026, Guangzhou, Çin, 28 Haziran - 03 Temmuz 2026, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Doi Numarası: 10.1109/isit62367.2026.11653959
- Basıldığı Şehir: Guangzhou
- Basıldığı Ülke: Çin
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
For the simple hypothesis testing problem with randomized detectors, the convex conjugate (i.e., the Legendre transform) of the type II error probability, as a function of the type I error probability, is shown to be the reflection through the origin of the primitive entropy spectrum. By applying the tail expectation formula to the primitive entropy spectrum, the type II error probability is expressed as a Riemann integral of the cumulative distribution function of the likelihood ratio. The derivation extends to tests between σ-finite measures in all non-void cases. The resulting characterization of the type II error implies state-of-the-art bounds on the type II error in terms of the type I error via Berry-Esseen theorem through a brief analysis.