MULTIPLE COMPARISON PROCEDURES FOR HIGH-DIMENSIONAL DATA AND THEIR ROBUSTNESS UNDER NON-NORMALITY

Abstract

This paper analyzes whether procedures for multiple comparison derived in Hyodo et al. (2012) work for an unbalanced case and under non-normality. We focus on pairwise multiple comparisons and comparison with a control among mean vectors, and show that the asymptotic properties of these procedures remain valid in unbalanced high-dimensional setting. We also numerically justify that the derived procedures are robust under non-normality, i.e., the coverage probability of these procedures can be controlled with or without the assumption of normality of the data.