A1629
Title: Simultaneous confidence regions of excursion sets
Authors: Fabian Telschow - Humboldt University zu Berlin (Germany) [presenting]
Armin Schwartzman - University of California, San Diego (United States)
Junting Ren - University of California San Diego (United States)
Abstract: Asymptotic statistical inference in the space of bounded functions endowed with the supremum's norm over an arbitrary metric space S is studied using simultaneous confidence regions of excursion (SCoRE) sets. These sets simultaneously quantify the uncertainty of several lower and upper excursion sets of a target function. Their connection is investigated to multiple hypothesis tests controlling the familywise error rate (FWER) in the strong sense, and it is shown that they grant a unifying perspective on 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. Additionally, the abstract setting allows refining and reducing the assumptions in recent articles on CoPE sets and relevance and equivalence testing using the supremum's norm as well as propose novel relevance and equivalence tests that control the FWER in the strong sense for Banach spaced data.
