The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations. Specifically, the asymmetric version of the problem is examined, where different requirements are placed on the two error probabilities. Accurate nonasymptotic expansions with explicit constants are obtained for the error probability, using tools from large deviations and Gaussian approximation. Examples are shown indicating that, in the asymmetric regime, the approximations suggested by the new bounds are significantly more accurate than the approximations provided by either of the two main earlier approaches -- normal approximation and error exponents.

翻译：本文研究了两种概率测度间的二元假设检验问题。基于独立同分布观测，我们推导了此类检验可达到的最优错误概率的新锐界。具体而言，我们考察了问题的非对称形式，其中对两类错误概率提出了不同要求。利用大偏差理论和高斯逼近工具，我们得到了具有显式常数的精确非渐近误差概率展开式。示例表明，在非对称情况下，新边界所建议的逼近精度显著高于以往两种主要方法（正态逼近与误差指数）所提供的逼近。