2018/04/16 by Michael Fauß, Abdelhak M. Zoubir, Fauss, Michael +3
Computer Science · Decision Sciences · Mathematics · #62C20 #Advanced Statistical Methods and Models #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Multi-Criteria Decision Making #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1804.05632
openalex publication_date 2018/04/16 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The paper deals with minimax optimal statistical tests for two composite\nhypotheses, where each hypothesis is defined by a non-parametric uncertainty\nset of feasible distributions. It is shown that for every pair of uncertainty\nsets of the f-divergence ball type, a pair of uncertainty sets of the density\nband type can be constructed, which is equivalent in the sense that it admits\nthe same pair of least favorable distributions. This result implies that robust\ntests under f-divergence ball uncertainty, which are typically only minimax\noptimal for the single sample case, are also fixed sample size minimax optimal\nwith respect to the equivalent density band uncertainty sets.\n