2022/05/11 by K. V. Harsha, Harsha, K. V., Jithin Ravi +3
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Information Theory (cs.IT) #Statistical Mechanics and Entropy #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2205.05631
openalex publication_date 2022/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a binary statistical hypothesis testing problem, where n independent and identically distributed random variables Zn are either distributed according to the null hypothesis P or the alternate hypothesis Q, and only P is known. For this problem, a well-known test is the Hoeffding test, which accepts P if the Kullback-Leibler (KL) divergence between the empirical distribution of Zn and P is below some threshold. In this paper, we consider Hoeffding-like tests, where the KL divergence is replaced by other divergences, and characterize, for a large class of divergences, the first and second-order terms of the type-II error for a fixed type-I error. Since the considered class includes the KL divergence, we obtain the second-order term of the Hoeffiding test as a special case.