High-dimensional multiple comparison procedures among mean vectors under covariance heterogeneity
High-dimensional multiple comparison procedures among mean vectors under covariance heterogeneity
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发表时间：
2021
影响因子：
3.2
通讯作者：
Masashi Hyodo;T. Nishiyama;Hiromasa Hayashi
中科院分区：
文献类型：
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作者：
Masashi Hyodo;T. Nishiyama;Hiromasa Hayashi
本文讨论了均值向量之间两种典型的多元多重比较过程：即成对比较和有对照的比较。在传统的多元分析中，这些多元多重比较过程是基于多元正态总体的Hotling的T2统计量构造的。然而，在高维设置中，例如当维度超过总样本大小时，这些方法不能应用。在这种情况下，Takahashi等人。(2013)在假设各组方差-协方差矩阵齐性的前提下，提出了渐近守恒的同时fi区间。不幸的是，当这一假设被违反时，这些同时发生的fi间隔不是渐近保守的。受此启发，我们基于L 2型统计量，在不假设方差-协方差矩阵是跨组齐次的前提下，得到了渐近守恒的fi区间。实证结果表明，所提出的同时fi间隔优于已有的方法。
In this paper, we discuss two typical multivariate multiple comparisons procedures among mean vectors: that is, 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 when the dimensions exceed total sample sizes, these methods cannot be applied. In such cases, Takahashi et al. (2013) proposed asymptotically conservative simultaneous confidence intervals 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.