Resampling-based simultaneous confidence intervals for location shift using medians

Abstract

A method for computing simultaneous pairwise confidence intervals for location shift is presented, based on the permutation distribution of the maximum absolute pairwise difference among all pairs. The method guarantees strong control of familywise confidence, and does not require assumptions about the form of the population distribution. Simulations compare the permutation procedure to a bootstrap procedure, as well as to the Tukey–Kramer procedure. Simulation results suggest the proposed permutation method produces intervals that maintain simultaneous coverage, and that can be more precise for heavy-tailed distributions compared to competing methods. The permutation intervals may be preferred for data from heavy-tailed distributions.