SCoRE Sets: A Versatile Framework for Simultaneous Inference
arXiv (Cornell University)(2023)
摘要
We study asymptotic statistical inference in the space of bounded functions
endowed with the supremums norm over an arbitrary metric space S using a
novel concept: Simultaneous COnfidence Region of Excursion (SCoRE) Sets. They
simultaneously quantify the uncertainty of several lower and upper excursion
sets of a target function. We investigate their connection to multiple
hypothesis tests controlling the familywise error rate in the strong sense and
show that they grant a unifying perspective on several statistical inference
tools such as simultaneous confidence bands, quantification of uncertainties in
level set estimation, for example, CoPE sets, and multiple hypothesis testing
over S, for example, finding relevant differences or regions of equivalence
within S. In particular, our abstract setting allows us to refine and reduce
the assumptions in recent articles on CoPE sets and relevance and equivalence
testing using the supremums norm.
更多查看译文
关键词
simultaneous inference,scope,versatile framework,sets
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要