SCoPE Sets: A Versatile Framework for Simultaneous Inference

02/10/2023

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by   Fabian J. E. Telschow, et al.

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We study asymptotic statistical inference in the space of bounded functions endowed with the supremum norm over an arbitrary metric space S using a novel concept: Simultaneous Confidence Probability Excursion (SCoPE) sets. Given an estimator SCoPE sets simultaneously quantify the uncertainty of several lower and upper excursion sets of a target function and thereby 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. As a byproduct our abstract treatment allows us to refine and generalize the methodology and reduce the assumptions in recent articles in relevance and equivalence testing in functional data.