SHARP ADAPTIVE AND PATHWISE STABLE SIMILARITY TESTING FOR SCALAR ERGODIC DIFFUSIONS

• 成果类型: Article
• 署名作者: Brutsche, Johannes; Rohde, Angelika
• 署名单位: University of Freiburg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2386
• 发表日期: 2024
• 页码: 1127-1151
• 关键词: functional data; EQUIVALENCE; approximation; inference

摘要

Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift b to some reference drift b0: At prescribed significance, we simultaneously identify those regions where violation from similarity occurs, without a priori knowledge of their number, size and location. This test is shown to be minimax-optimal and adaptive. At the same time, the procedure is robust under small deviation from Brownian motion as the driving noise process. A detailed investigation for fractional driving noise, which is neither a semimartingale nor a Markov process, is provided for Hurst indices close to the Brownian motion case.