Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in \cite{wu2022score}. We analyze the performance of this score-based hypothesis testing procedure and derive upper bounds on the probabilities of its Type I and II errors. We prove that the exponents of our error bounds are asymptotically (in the number of samples) tight for the case of simple null and alternative hypotheses. We calculate these error exponents explicitly in specific cases and provide numerical studies for various other scenarios of interest.

翻译：基于得分的统计模型在现代机器学习、统计学和信号处理中扮演着重要角色。针对假设检验问题，\cite{wu2022score} 提出了一种基于得分的假设检验方法。我们对这一基于得分的假设检验流程的性能进行了分析，并推导了其第一类和第二类错误概率的上界。我们证明，在简单原假设和备择假设情形下，我们的误差界的指数在样本数趋于无穷大时是渐近紧致的。我们显式地计算了特定情形下的这些误差指数，并针对其他各种感兴趣的场景提供了数值研究。