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重要角色。针对假设检验问题，文献\cite{wu2022score}提出了一种基于得分的假设检验方法。我们分析了该基于得分的假设检验程序的性能，并推导了其第一类与第二类错误概率的上界。对于简单原假设与备择假设的情况，我们证明这些错误界的指数在样本数趋于无穷时是渐近紧致的。我们显式计算了特定情形下的这些错误指数，并就其他各种感兴趣的场景提供了数值研究。