ArticleEntropy (Basel, Switzerland)2026
Weighted Chernoff Information and Optimal Loss Exponent in Context-Sensitive Hypothesis Testing.
Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
We study binary hypothesis testing for i.i.d. observations under a multiplicative context weight. For the optimal weighted total loss, defined as the sum of weighted type-I and type-II losses, we prove the logarithmic asymptotic Ln∗=exp{-nDCw(P,Q)+o(n)},n→∞, where DCw is the weighted Chernoff information. The single-letter form of the exponent relies on a structural assumption that the weight factorises across observations, φ(x1n)=∏i=1nφ(xi); this restriction is essential for the single-letter representation and should be distinguished from the weaker qualitative description "multiplicative context weight". The proof embeds the weighted geometric mixtures φpαq1-α into a likelihood-ratio exponential family and identifies the rate through its log-normaliser. We also derive concentration bounds for the tilted weighted log-likelihood, obtain closed forms for Gaussian, Poisson, and exponential models, and extend the exponent characterisation to finitely many hypotheses.
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