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A0683
Title: On the multiple comparison procedures among mean vectors for high-dimensional data under covariance heterogeneity Authors:  Takahiro Nishiyama - Senshu University (Japan) [presenting]
Masashi Hyodo - Kanagawa University (Japan)
Hiromasa Hayashi - Osaka prefecture University (Japan)
Abstract: Two typical multivariate multiple comparisons procedures among mean vectors are discussed: pairwise comparisons and comparisons with a control. In traditional multivariate analysis, these multivariate multiple comparisons procedures are constructed based on Hotelling's $T^2$ statistic in multivariate normal populations. However, in high-dimensional settings, such as when the dimensions exceed total sample sizes, these methods cannot be applied. In such cases, asymptotically conservative simultaneous confidence intervals have been proposed under the assumption of homogeneity of variance-covariance matrices across groups. Unfortunately, these simultaneous confidence intervals are not asymptotically conservative when this assumption is violated. Motivated by this point, we newly obtain asymptotically conservative confidence intervals based on $L^2$-type statistic without assuming that the variance-covariance matrices are homogeneous across groups. Empirical results indicate that the proposed simultaneous confidence intervals outperform existing procedures.