Confidence regions for univariate and multivariate data using permutation tests

Confidence intervals are central to statistical inference as a tool to evaluate the type I error risk at a given significance level. We devise a method to construct confidence intervals using a single run of a permutation test. This methodology is extended to a multivariate setting, where we are able to handle multiple testing under arbitrary dependence. We demonstrate the method on a weather data set and in a simulation example.

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