This paper analyzes whether procedures for multiple comparison derived in Hyodo et al. (2013) work for an unbalanced case and under non-normality. We focus on pairwise multiple comparisons and comparisons with a control among mean vectors, and show that the asymptotic properties of these procedures remain valid in an 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

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... e controlled with or without the assumption of normality of the data.