Confidence regions for univariate and multivariate data using permutation tests

TL;DR

This paper introduces a novel permutation test-based method for constructing confidence intervals in univariate and multivariate data, effectively managing multiple testing issues under arbitrary dependence.

Contribution

The paper presents a new approach to create confidence intervals using permutation tests, extending it to multivariate data with multiple testing correction under arbitrary dependence.

Findings

Effective in weather data analysis

Handles multiple testing under arbitrary dependence

Validated through simulation studies

Abstract

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.