Hypothesis Testing with the General Source

2000/04/19 by Te Sun Han, Han, Te Sun
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.math/0004121

34 pages, 0 figures

openalex publication_date 2000/04/19 · arxiv created 2000/04/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in doing so is first to convert all of the hypothesis testing problems completely to the pertinent computation problems in the large deviation-probability theory. It turns out that this kind of methodologically new approach enables us to establish quite compact general formulas of the optimal exponents of the second kind of error and correct testing probabbilities for the general sources including all nonstationary and/or nonergodic sources with arbitrary abstract alphabet (countable or uncountable). Such general formulas are presented from the information-spectrum point of view.

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