High-Dimensional MANOVA Via Bootstrapping and Its Application to Functional and Sparse Count Data
High-Dimensional MANOVA Via Bootstrapping and Its Application to Functional and Sparse Count Data
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DOI：
10.1080/01621459.2021.1920959
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发表时间：
2020-07
影响因子：
3.7
通讯作者：
Zhenhua Lin;Miles E. Lopes;H. Müller
中科院分区：
文献类型：
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作者：
Zhenhua Lin;Miles E. Lopes;H. Müller
摘要：我们提出了一种通过涉及样本均值向量差异的引导最大统计量来解决高维多元方差分析问题的新方法。所提出的方法通过针对总体平均向量的差异构建同时置信区域来进行。它适合同时测试可能超过两个总体的几对平均向量的相等性。通过利用相关应用中自然特征的方差衰减特性，我们能够为高斯近似、自举近似和测试大小提供无量纲和近参数收敛率。我们通过函数数据和稀疏计数数据的方差分析问题演示了所提出的方法。所提出的方法在模拟和一些实际数据应用中显示出良好的效果。
Abstract We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a natural feature in relevant applications, we are able to provide dimension-free and nearly parametric convergence rates for Gaussian approximation, bootstrap approximation, and the size of the test. We demonstrate the proposed approach with ANOVA problems for functional data and sparse count data. The proposed methodology is shown to work well in simulations and several real data applications.